What to expect... In the mind of a beginner, starting something new let alone a martial art, is an intimidating thing. The key to success is accepting that you know nothing at the beginning and forgetting everything you think you know right at the start. Your instructor and team mates are there to help you. At any good school, they will support you and show you how to get started. Even though a lot of Brazilian Jiu Jitsu practice is based on sparring, the likelihood of getting injured from it is very low.
Why is it like this? The Jiu Jitsu and martial arts culture is very zen for starters, everyone is a beginner and is also still learning. If you are in a school where on your first day your teammates are trying to show you how good they are, you are in the wrong place. At the end of class you should always feel as though you have learned something or have improved on a skill you already have.
Your first day will likely be comprised of learning basic positions and drilling a few simple techniques. If you are in a situation where you are "rolling" for the first time, the session should be based on holding a certain basic position until you are comfortable to move on.
Tapping out... This is something everyone does and for good reason. Jiu Jitsu isn't like striking martial arts where there isn't the opportunity to tap out - its completely safe. When things are too much and you hit your limit, you tap and start over. Tapping out should never be associated with "giving up", rather tapping out is starting over. In fact, its a great opportunity to ask questions and find out what you did to get yourself in the position to tap. When you are learning, tapping out is a necessity. If you are not tapping, you are not learning.