Swim meets are actually fairly simple, but there are some confusing elements that can take a little while to get the hang of. First thing you need to know: A meet is where you race. Although there are different levels of meets, this is where you'll want to perform at your very best, because this is where you will get times.
A meet is structured within different events. An event is what you are swimming, such as the 50 freestlye or 100 backstroke.
Within the events, there are different heats. This just means what group you are swimming in. If you are in heat one, you are in the first group of people swimming that event.
Finally, within each heat, there are the lanes. Everyone gets their own lane to swim in, and typically there are 6, 8, or 10 lanes in a pool.
In some meets, you can get in no matter what time you swim, but in others, such as State, Zones, Futures, NCSAs, Junior Nationals, Nationals, or even the Olympic Trials, you have to qualify for these. To qualify, you have to reach a certain time cut (or time standard), and then you can go to these meets.