Maybe you're just not connecting it with the broader series of party conventions that happen every 4 years. Maybe you've seen them on TV but never labeled them as such?
Every year, each party has a national convention in some US city. Most notably, of course, are the "Democratic National Convention" and "Republican National Convention," but other national parties also hold conventions. But I'll focus on the Democrats and Republicans.
For each of these parties' conventions, there are delegates sent from all over the country who (somewhat indirectly) represent their home areas and vote for a particular candidate to run under the party's banner for President.
The conventions feature lots of speeches by various members of the party (mostly politicians), which are all held in a large event space like a sports arena. (If you search Google Images for famous (democratic OR republican) convention photo+convention+photo&safe=off&tbm=isch&tbo=u&source=univ&sa=X&ei=dk7eVNzDMYibNuLsgoAI&ved=0CB8QsAQ&biw=1366&bih=704), you mind find that these look familiar.) I'm not sure if there are other smaller events also going on throughout the day.
The conventions are also known for their nighttime parties where politicians and affiliated groups are often hosted by their favorite corporate donors. (See here and here.)
The conventions are typically broadcast in full on C-SPAN, while the larger TV and radio networks only tend to broadcast the most high-profile speeches during prime time.
For example, the 2004 DNC is where then-Illinois State Senator Barack Obama offered a famous (televised) keynote address that brought him into the national spotlight, leading to his short time in Congress and his presidential run.
Meanwhile, the 2004 RNC was held right here in NYC at Madison Square Garden and is famous for its massive protests, massive police presence and police action, and the ensuing class action lawsuit against the NYPD by the many protesters and bystanders who were rounded up, illegally detained, and otherwise mistreated.
By the way, to further complicate things, in addition to the word "convention," DNC also stands for Democratic National Committee & RNC also stands for Republican National Committee.