Things have really changed when it comes to pitching in baseball. A team used to send a couple of starting pitchers out (Sometimes with the same starter for both games of a double header!), and relievers were just other starters basically who could go in for injuries or if a starterwas really taking it on the chin. These days, teams play in very small stadiums compared to what they used to have in the league, and baseball has become less of a game and more of a business. Seeing as how a lot of owners are businessmen, they're looking to protect their investments, and their biggest investment is usually in the starting pitchers. Thus, you get relievers to come in early if there's a sign of trouble with the starters, and closers who (You guessed correctly here) come in to close out a close game in the last inning or two.
Speaking as a former pitcher, it's really amazing how much pressure you can put on your arm performing some of these pitches. Even the simple fastball has nearly become a thing of the past, with all kinds of varieties of it becoming more prominent. To be successfull these days, your pitches need movement, and that extra curve on the ball is at the expense of more pressure on a lot of little pieces of stuff in your arm. It's not a coincidence that the majority of the really successful pitchers that last a long time these days are the ones who are soft throwers relying on control (Greg Maddox/Tom Glavine). Some power pitchers can last like Nolan Ryan, who simply had an amazingly resilient arm, or Roger Clemens, though his longetivity is now being called into question. More often with the hard throwers, you have a career like Randy Johnson or Pedro Martinez, with a great start, a slow decline, then injuries completely derailing the career.
Once you get out of your little league (Maybe high school) years, nobody will pitch their starters too much because they don't want to risk injury. So, kids are generally put on a pitch count (Meaning they have a set number of pitches they are allowed to throw in a game, hit that number and they come out, no matter what). Some little leagues around here have mandatory pitch counts, so as a manager, you don't even get a choice in the matter.
Once the idea of limiting overwork on pitchers arms came along, the relievers started to become more prominent. The same rules generally apply to them, but the kicker here is that since relievers tend to not pitch as regularly, or as long, their arms will tire more quickly than starters (For the most part, there are some relievers that can pitch a couple of innings a day all year it seems like, but those guys are rare)
so you need to have at least 4-5 of them to be available in case you need more than an inning or two out of them. You also have the whole matchup thing, which says you need to have both lefthanded relievers and right handed relievers to match up against the batters.
The closer idea is very new, with regular use only coming in the past few decades. The idea here is simple. To put a guy in there with only a few outs to get, who will simply overpower the batters he faces. You don't want a soft thrower here, because you want to keep men off the bases as much as possible since he'll be pitching with a 0-3 run lead. You want a guy who can come in with 1 out in the bottom of the 9th with the bases loaded, and you're up by one run, and you'll be reasonably sure that the first guy he faces will get struck out. Because this pitcher tends to be the hardest thrower on your team, you don't want to overwork him, he's generally in for an inning, maybe less, maybe a bit more. And they often won't use the closer on more than 2-3 consecutive days. Again, individual circumstances can vary, but teams generally follow those guidelines.
The big issue these days is protecting the investment. Often, a team's biggest investment is in pitching. They command the most money and the long deals. Usually, it's the starters who get the most, followed by closers, though some relievers are getting up near that closer pay. As a manager, you don't want to have to go to the owner and tell him that the $15-20 million he just spent on that new starter was wasted because you shredded his arm, so you'll do what has to be done to try and make sure that doesn't happen.
