Because it becomes increasingly hard for writers to come up with new and unique ideas. When there are 12-20 episodes a season, you can really run out of stuff fast.
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I think because they usually have maybe 2-3 plots in development at the time they do the premiere. And those plots are meant to be slow in developing, like the "Save the Cheerleader" theme in Heroes, so that that first plot takes most of the first season, as we learn to get to know the characters and their world.

Then, the next season, they develop that a bit more with a twist to the plot. If the writers are really good, they can then add another direction for the show before it moves too far away from its roots. In some cases, like the Stargate franchise, they can go through 11 seasons and a spinoff that goes through several more seasons and still keep up the excellence.

I think that sometimes, though, those initial discoveries about characters are part of what makes it so interesting, just like when you're dating someone new. Shows that make that a major part of their mix can find it hard to have their viewers adjust to other equally important elements of a good show, once those discoveries and revelations have wound down.
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I don't think they peak at that time... I think a show needs at least 4 or 5 seasons to completely come to fruition. LOST is a perfect example of that.

I think Firefly, Dead Like Me and Wonderfalls are great examples of shows that were not given the opportunity to play out their stories.
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To keep you interested, and keep you coming back for more. To keep the cash flow going, if they lose their viewers the shows are over and people move on to the next show. Keep you on edge, emotionally over charged, anxious, can't wait for the next set of series.
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The first season of any series is really just one long pilot sectioned off into several episodes; if a series lasts beyond the first season nowadays, it is a sign that the writers have found a target niche.

Like with anything new, television series struggle to find their audience in the first season, further develop plot lines and characters in the second season, and then introduce major turning points in the third to fifth seasons.

Also, you may notice, that most new series are not always placed in the primetime slots, unless they have a "star" cast, or a heavily promoted theme which is already supported by trends in Hollywood (see Heroes). As is such, the more limelight a show gets, the more primetime it will get, the more sponsors it will get, and the more ratings and dollars it will recieve to hire better writers and attract guest stars.
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When we are watching first or second season, mostly we are learning about the characters. Writers tries to gradually elaborate on each character more and more, and once you become to third season - you know the characters very well. After that, it's the story.

However, once the characters' behaviors have been introduced, writers have to be very careful about story.

Another reason is that some stories are completely depending on a previous episode - If the viewers missed the previous episodes, they'll eventually get bored and give up.
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When a series is new, it doesn't get the "word of mouth" advertising like a series that's been around for a couple of years does. The more people talking about the show, the more people tune in to see what it's all about.
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Shows tend to peak around the third season because the third season tends to be the sweet spot when the characters and plot have fully developed and the script writers still have fresh material.
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Plot. By that time, characters are developed, fans are invested and writers are on a roll.

The reason it's difficult for shows to last as long as, say, Friends, is because the story lines get offtrack and start to take away from the real reason the show was popular in the first place. After a while, there are so many directions you can go with fully developed characters.

So, the first couple seasons aren't so popular because it's still new. The characters themselves have yet to get into the swing of things.
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A lot of shows these days never make it past their first season. If they make it to their second and third seasons the writers become more comfortable with the path they are taking with the storyline(s). The characters become more familiar and interconnected, more relatable. Word of mouth gets people wondering about the show and the popularity increases so therefore they peak in rankings.

The shows also find a niche in later seasons, they become the show everyone watches on a certain night of the week. They become part of a routine.
Source(s):
Top of mind

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After a fan based is established, writes can experiment more with the plot, most of the time leading to higher ratings.

If this would be done in the first season, views could easily get lost and lose interest.
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After the 2nd season the writers are trying to extend the show and go into deeper plot lines that take more than a season or 2 to develop
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