The reason political parties use delegates is probably so that the dropping out of a candidate can be dealt with. No delegate is required to keep voting for the same person for the same office at successive meetings. However, delegations are chosen to have a proportional representation of nominees for the most important office that's up for election that year. E.g., in 2010, there was no presidential election, so the Colorado Democratic Party could have chosen either the gubernatorial race or the senate race. We had one nominee for governor (John Hickenlooper), but two nominees for senator (Michael Bennet and Andrew Romanoff), so delegates had to identify with either Bennet, Romanoff or Undecided at each stage.

In the Democratic Party, delegates are chosen at previous party meetings. The meeting that's open to all registered Democrats is the caucus. At the caucus, delegates are chosen to serve precincts at county meetings and state legislative-district meetings. At the state house meeting (at least for us in Colorado), delegates can be chosen to represent their house district at the congressional-district and state meetings. At the state meeting, delegates can be chosen to repesent their state at the national meeting (the DNC).

I live in a large county, so I go to a county meeting that breaks up into district meetings. The hierarchy probably works the other way around in places where counties tend to be smaller than legislative districts.

The process for going to the next level is this: At the caucus, you record which candidate you're in favor of. Using the totals, the precinct committee figures out how many of the precinct's attending voters in favor of each candidate should be sent to the next level. Those delegates are then elected from among the attending members that were recorded as favoring the associated candidates. The same thing happens at the house district meeting. Which precinct you're from no longer matters at that point. At the state meeting, if national delegates are to be chosen, they'll be elected by the whole assembly, and there are a lot of them, so there's a long ballot. When the numbers get large like that, the Democratic Party requires that men and women be represented in equal numbers, so the ballot is actually split by gender. (I foresee some interesting discussions about transgendered people in the next decade.)

In the old days (at least as late as 1944), presidential nominations weren't made until the national convention, so having humans gathered in one place was absolutely necessary for choosing a candidate and unifying the party behind him.