A league is basically a racing series or championship with any given car and track combinations. There are lots of leagues around, and they are made up of all kinds of drivers from different skill levels. The leagues themselves are sometimes amateur ones, or professional ones, there is a lot of variation. And they are fun! Actually, league racing is usually more fun than your usual online/public racing. In leagues you usually have the series of events like Qualification and the Race with a fight for points in the championship. And there are almost always a set of rules that you follow, and all in all, it is the best way to get some good clean racing for the day. And you gain a lot of experience from a league, seeing how other people drive and you meet a lot of new people
A team... well that is like with any sport, a team is a group of drivers that share the same team name/skin/website/goal, etc... and there are lots of teams in LFS. You can always look around for a team in your area, and see which one fits you best. There are quite a few fast teams, but if you aren't very fast, there are plenty of teams that fast 'enough' and just like to have fun.
The main aspect of both team and a league here... they are FUN.