Let's imagine that your kid just started playing soccer for the first time, and while watching the adorable little rugrats chase the ball across the field, you think to yourself, "Well, I'd better figure out what this sport is about, since Billy loves it so much*"
So you turn on the NBC Sports Network or ESPN2 or the Fox Soccer Channel or some damned thing and find a soccer game. If you're lucky you find a European soccer game**, and you're astonished at its style, precision and beauty.***
If you're slightly less lucky you find an American soccer game, played by one or more teams from the MLS. I'll offend... somebody... by suggesting that MLS soccer is about on a par with a third-division European league. The MLS All-Stars regularly lose to Manchester United, but the games are sometimes competitive. I'm sure the All-Stars could beat a second-tier English team, and that suggests to me that the Colorado Rapids might be able keep up with Scunthorpe United**** or Exeter City.
Perhaps FC Dallas is playing Sporting Kansas City, or you may see the LA Galaxy play Tigres UANL of San Nicolas, Mexico. You might even see DC United against the Rochester Rhinos (Really! The Rochester (NY) Raging Rhinos are a minor-league soccer club).
You might be confused. Although there are three Canadian teams in MLS, there aren't any Mexican teams. What's the Galaxy doing playing Tigres? And the Rochester Rhinos are an NASL team -- the US's semipro minor leagues -- not MLS.
Several major competitions go on in parallel in North America every year. (For simplicity's sake I will focus on MLS games and ignore things like Mexico's Primera Division regular season.)
The first is the MLS regular season. This runs from March through December; each of the 19 teams in the MLS plays 34 games exclusively against other MLS teams. The top 10 teams in the league go to the MLS Cup playoffs, culminating in a single champion.
You may see teams play in the CONCACAF***** Champions League. The top 4 US MLS teams in any given year participate in the CCL the following year, and play against the top teams from Mexico, Central America, the Caribbean, and Canada. This would be why you'd see Galaxy play Tigres.
Finally, you might be seeing part of the Lamar Hunt US Open Cup. This is a knockout tournament open to the top teams from all 5 layers of US Men's Soccer, from amateur adult clubs up through MLS teams. This would be why you'd see DC play Rochester. (And Rochester did beat Colorado to win the cup back in '99).
These do all go on in parallel. LA Galaxy might play a CCL game on Tuesday, an Open Cup game on Thursday, and an MLS game on Saturday, all in one week. That can lead to some of the more successful clubs complaining of exhaustion near the end of the season, while they are playing more games than competitors who didn't do well enough to get into the CCL, for instance. Many clubs use the CCL and Open Cup as a way to get their prospects more touches and rest their premiere players; LA Galaxy may not put Landon Donovan and David Beckham on the field against Addison United of Vermont.
* At this point, Billy actually just loves the juice box and bag of pretzels he gets after the game, but that may change.
** It irritates me that American soccer correspondents insist on calling a game a "match" and a field a "pitch" because that's what they're called in England.
*** You're also astonished at the audacity of players diving to draw foul calls when they haven't been touched. Doubly so if they're Italian.
**** Take that, obscenity filters
***** The North American continental soccer confederation, which includes the US, Canada, Mexico, Central America, and the Caribbean