I was looking at your bulletin and on the blog and I saw the phrase Nineteenth Sunday after Trinity, or Trinity 19. What does that mean? 
I am giving you two answers here. A very short one now, and much fuller one afterwards. If you have any concerns about this practice, please read the fuller explanation below.

Quick Answer

The quick answer is this: The (whatever number) Sunday after Trinity refers to Trinity Sunday, which in the Church Year, comes the week after Pentecost. Trinity Season is a grab bag of directed readings and songs. It fills the weeks between Pentecost and the First Sunday of Advent, at which time we start looking forward to Christmas.
More broadly, the Church Year is just a tool that can either be used or not. In and of itself it means nothing and is not sacred. Used as it was intended, it directs the Christian to particular passages throughout the year, based on the various events of Jesus life: His birth, His death and resurrection, His ascension, and when He sent the Spirit to us on Pentecost. It is basically a large-scale version of the Bible-in-One-Year. The only difference being, instead of just an interesting way to read the Bible, the Church Year gives us many, many opportunities to gather as a Church body and feast and sing till the cows come home. 

Longer Answer

Before answering that question more fully, I want to preface it with a few verses that must be fixed in your mind, and in mine, as we talk about seasons and calendars and special days. 
One person esteems one day as better than another, while another esteems all days alike. Each one should be fully convinced in his own mind. The one who observes the day, observes it in honor of the Lord. The one who eats, eats in honor of the Lord, since he gives thanks to God, while the one who abstains, abstains in honor of the Lord and gives thanks to God. For none of us lives to himself, and none of us dies to himself. For if we live, we live to the Lord, and if we die, we die to the Lord. So then, whether we live or whether we die, we are the Lord's. (Romans 14:5-8)
And again:
Therefore let no one pass judgment on you in questions of food and drink, or with regard to a festival or a new moon or a Sabbath. These are a shadow of the things to come, but the substance belongs to Christ. (Colossians 2:16-17)
In any discussion of the liturgical Church Year (for that’s what this is) these verses must form the foundation of our thoughts. Days and seasons and years and months and holidays and feasts are nothing in themselves. The calendar is a mere tool. If it doesn’t fit your particular project, drop it and use another. The tool itself is not sacred. 
With that said, why have I been paying attention to all these Sundays after Trinity? And before that Advent, and Epiphany and the Wilderness? Because days and months and years are woven quite inextricably into the fabric of our life, you and I have learned from an early age to count them. We have given them names. We look forward to certain months with eager anticipation; for we know what kinds of things usually happen in those months: favorite weather patterns, holidays, birthdays, sports events, etc. You and I have learned these habits from before we could think for ourselves, and so they have come into the house of our second nature and established themselves as the furniture. 
Have you ever stopped to think about who structured our year? Who gave us Labor Day, Memorial Day, Columbus Day, Veterans Day? We will structure our year somehow, guided by someone. The question posed by the Church Year is this: Why not let our year be guided by the life of Jesus? I will emphasize again, the question is a “Why not?” - not a “You must”. I hope that remains clear. Why not define our seasons in such a way that reminds us that Jesus is coming again? Why not have a season of reflection on the work of Christ in His Earthly ministry, a season defined by praise and celebration leading up to the Resurrection? 
We are products of our habits. But what informs and directs our habits? As Christians, we believe the Word of God should be behind everything that we do. And there are many tools God uses to do this. The Church Year is just one of them. Again, the tool itself is not special in and of itself. The important thing is what God can do with it. The goal is becoming more like Christ. If the Church Year can help, then praise God. If not, pray and ask God to use whatever means He would to make you more like His Son.
So why do I appreciate, and use, the Church Year? Personally, I find it to be a refreshing and invigorating escape from the craziness of our consumeristic culture. We all love to celebrate Christmas and Easter, don’t we? For me, placing them in the context of Advent and the Wilderness counteracts the kitsch our modern culture has used to distract us from the real import of these central Christian holy days (or holidays if you prefer). Celebrating Advent and the Wilderness helps to direct my thoughts away from the hustle and bustle and shapes my habits to around the real joy and real festivity of the Incarnation and the Resurrection.
So you still haven’t answered my question about Trinity Sunday? What gives? 
Our great-great-granddaddies in the Reformation cleaned house when it came to feast days and holy days. But they continued to celebrate a few special days and seasons throughout the year, that centered on the key points of the life of Jesus. Those days and seasons are Advent, Christmas, Epiphany, Holy Week (Palm Sunday through Good Friday), Resurrection Sunday, Ascension Sunday, Pentecost, and Trinity Sunday and Season. So what do all these days and the various seasons between refer to?
Advent: The four Sundays before Christmas. It is the beginning of the Church Year, as it celebrates the season of longing and expecting the Christ to come, born of a woman. The Second Coming is also emphasized during this season.
Christmas Sunday: We celebrate the Incarnation
Epiphany: 6 Sundays celebrating the coming of the Magi, the Baptism of Jesus, and the Transfiguration.
Wilderness: This is a sticky one. Most people know this season as Lent. However, I have used the name Wilderness because that is what the original term used to mark these 5 Sundays referred to (Quadragesima = 40 days). Originally it was a season celebrating the fact that the light and life of the Resurrection was coming (Lent = Spring). It celebrates the 40 days of Jesus in the wilderness, which was a microcosm of His entire 3 year ministry. The way this season should be celebrated therefore is with gratitude and joy, realizing that the active obedience of Jesus during His ministry has been given to us, so that we might stand before the throne of God. In other words, we should all eat more chocolate, not less.
Passion Week: Starting with Palm Sunday, through to Good Friday, the last week of Jesus pre-resurrected life is celebrated. 
Resurrection Sunday and Season: He is Risen! He is Risen Indeed! After this Sunday, there are 5 Sundays that lead to...
Ascension Sunday: Celebrating Jesus’ Ascension on the clouds of Heaven, and taking His seat at the right hand of the Father.
Pentecost Sunday: Celebrating Pentecost, the Church’s official Birthday, the day the Holy Spirit descended on the disciples.
Trinity Sunday and Season: Following Pentecost, almost 30 Sunday’s are left before Advent picks up again. Now part of the reason for these days is a way to direct our Scripture reading, and do so in a way that allows everyone to be on the same page. The 30 Sundays of Trinity are, for all intents and purposes, a miscellany, a grab bag of topics not covered in the first 20 weeks of the year. 
That in a nut shell (I know...a pretty big nut) is what we are paying attention to in the Church Year. One final reason why this is special. Our fathers in the faith, for almost 2000 years have been celebrating something similar to what I have just laid out. These days, then, have become the ancient landmarks of our faith, reminding us on a yearly basis, the full import of our story as a people. For we are a new humanity, a new race, formed and fashioned to serve and praise God. May our days never forget that we belong to the Lord. May our seasons be constantly reminding us that we are being shaped by the Word of God into the image of Jesus, our King.