Not a whole hell of a lot.
In the old days, before past-paced telecommunications, exit polling, and constant media coverage, there often wasn't a "clear" victor ahead of time, so the delegates would actually make speeches, cast votes, and eliminate candidates until someone won the nomination, which could take several ballots (at the Libertarian Party Convention two months ago, they actually did this: it took five ballots to establish a winner). The winner then gives an acceptance speech to close the convention.
They would also vote to choose a vice-president, and vote to approve "planks" of the party's platform for the coming election. However, these days the presidential candidate chooses his own running mate, and the party platform is established by a small subcommittee of each party that meets independently of the national convention.
These days, all that really happens is people make speeches to support the presidential candidate, and the balloting and acceptance are simply pro forma. Increasingly, even statements of policy and platform are left to media press releases, and the speeches are just to help with the candidate's "message" and appeal to the electorate. These speeches have become something of a spotlight for up-and-coming figures in the two parties; Bill Clinton spoke in 1988 and Colin Powell in 1996, and Barack Obama's speech at the 2004 Democratic Convention is widely credited for propelling him onto the national stage.
One of the traditions that is kept alive is the wearing of straw boaters, those funny hats with the ribbon around the brim. A budding tradition is that of lobbyist parties, where major funders of the political parties organize large, exclusive fetes after hours; who gets invited and who shows up at these engagements is a telling summary of who has influence in Washington.