I haven't been in seminary for years, but I have been asked this question on occasion, so I will explain. For more details, please visit: http://seminary.lds.org/?lang=eng
Seminary is a program to help students in high school develop their testimonies of their Savior. The students study a different book of scripture every year. Old Testament, New Testament, Book of Mormon, and Doctrine in Covenants each are focused on during one year of high school.
The time when students attend seminary differs. In areas where there are a high percentage of Mormons (members of the Church of Jesus Christ of Latter-day Saints), release-time seminary can be held during school as a free period. This is how I experienced seminary. This time for seminary is usually seen in places like Utah, Idaho, and some parts of Arizona. Going to seminary wasn't much of a sacrifice for me. It was nice to be able to have a break from school and feel the spirit, but it was held in a building across the street from my high school within easy walking distance. It didn't really take much effort to go there.
However, for those young members of the church who live in an area with many people who aren't members of the church, they are asked to attend what is called early-morning seminary. Usually this is around 5-6 in the morning. I have many cousins and friends who experienced this kind of seminary. I am very impressed with their dedication in attending these meetings.
Anyone who has high school students knows how hard it is to wake most of them up. I was no exception. I slept until the very last possible moment, and then bolted to school. (It helped that the school was in walking distance of my house as well.) I think it is pretty amazing that so many young people (and their parents) sacrifice sleep in order to go and talk about scriptures super early in the morning.
Why would they sacrifice so much?
For me, it wasn't really a sacrifice. I love seminary, and I loved learning the scripture stories and about my Savior. I think for those kids who have to get up early, they do it for the same reasons, and maybe they don't view it as a sacrifice either.
Some of the most powerful spiritual moments of my younger life occurred while I was in seminary. I had teachers that encouraged us to ask questions, pray about the gospel, and read the scriptures. While I was in seminary, I never missed a day of scripture reading. It was amazing to hear the testimonies of other young people my own age who were going through similar things that I was going through.
Seminary is a good introduction to the gospel. Youth are faced with constant moral dilemmas, and it is easy for them to feel confused and powerless. Sometimes, that little bit of light in the morning (or during the day) can really bring a spirit of peace.
I am grateful for my experiences in seminary, the scriptures that I memorized, and the things that I learned. They had some cheesy videos, but that was kind of fun too. Those videos often helped to emphasize important points of doctrine.
High school can be a pretty confusing and selfish point in life. I think I am a better person for attending seminary, and I have a better mastery of the scriptures.