It's a question Protestants often ask Catholics, and in Sunday's homily, Fr. Welzbacher provided some perspective on the Catholic teaching.
The answer, fundamentally, lies in this quote from Sunday's first reading: "And you," Paul says, "became imitators of us and of the Lord, for you received the word in much affliction, with joy inspired by the Holy Spirit, so that you became an example to all the believers in Macedonia and in Achaia." (1 Thessalonians 1:6-7; emphasis added)
"Imitators of us and of the Lord." This is not the first time Paul speaks of imitation; in his second letter to the Thessalonias he repeats this, saying, "You know how one must imitate us." (3:7). In his letter to the Phillippians, he says "join in imitating me and observe those who live according to the example you have in us." (3:17)
Imitation of Godly people is a good thing. As John says in 3 John11, "Beloved, do not imitate what is evil, but what is good." And what else is important in this respect is to remember that imitation of the saints is for the praise and glory of God, by Whose grace men and women assertain the holiness that He desires of us. We do honor to God by following His saints, in much the same way as our behavior can often reflect upon our parents, who are given credit for the way in which they brought us up.
All right, Fr. Welzbacher says, Protestants may concede the point, that it is a fine thing to admire the saints. But then what about the statues, the icons, the pictures in the churches. Is that not a form of idolatry? Indeed not, Fr. W. replies, for we do not worship the statues. We do not believe that the statues are living, that the person who they represent dwells in the icon, that pictures make that person present with us. (This does not, of course, refer to miraculous apparations when statues appear to weep tears or shed blood; this should be understood as precisely that, miraculous, an intervention by God into that which is ordinary, to make it extraordinary. To the extent that statues "come alive," they do so only as the power and presence of God cause it to happen.)
Instead of idolatry, think of it as a family portrait. For we are all brothers and sisters, members of the Body of Christ, united within His Church. And in the same way that we cherish family portraits, photos of our parents and sibilings and other loved ones, so do we cherish those of our spiritual relatives, Jesus and Mary and the saints. A man keeps a portrait of his wife on his desk at work to remind him of her, so that even when she is far away in body she may be near to him in spirit. A picture of a special event, a small piece of sculpture that is a memento of a particular place; all these serve to remind us, and to recreate the spirit, the feelings that were originally present in that time and place.
This is nothing new; iconoclasm (literally, image-breaking) was present in the eighth and ninth centuries and was condemned as heresy at the second Council of Nicaea in 787. (It should be noted that this was long before the Reformation or other schisms which the Church has endured; by the late 800s one could say that it was understood by the universal Church that iconoclasm was wrong.)
So we take the saints as our role models. (Something I've written about extensively, so it shouldn't surprise you that I conclude by returning to this theme.) We emphasize them by following their example, something we do at the express command of Paul. We pray to them to intercede for us before the Lord, as we ask our friends and loved ones to pray for us during times of need. For if your spouse or parent or closest friend's prayers can be beneficial, how much more so when that person resides in Heaven, with Jesus at the right hand of the Father?