Seth Masket, a political scientist who writes at the Mischiefs of Faction blog, explains why political conventions matter more than you might think.
This is the part of the election cycle where normal Americans (read: not political junkies) begin to pay attention to the candidates, the parties, and the issues, and the conventions are a big part of how that happens.
Along these lines, conventions serve as an opportunity for a party to present its candidates and its stances to the general public. Those who only learn about the current election from advertisements are getting a somewhat abbreviated and decidedly negative perspective; the conventions are the parties' chance to define themselves and lay out their arguments for why they should be in charge. We also get to see some of the up-and-coming candidates in a party; the next two weeks will give most Americans their first opportunity to hear from some of the likely 2016 presidential candidates.
Conventions also provide a rare opportunity for gathering something close to the entire party (depending on how one defines that) under one roof. That is, a national convention includes delegates, donors, activists, interest group members, officeholders, opinion leaders, and candidates from all levels of government. It's a chance for some of these people to meet each other and discuss issues, strategies, future candidates, etc. Oh, and if you happen to research parties, this is a pretty great opportunity to talk to a wide range of party members.