What are the benefits of doing the radiant quests from the thieves guild?

The special quest for a particular city is unlocked after you've done 5 radiant quests in that city. When you complete a special job in the city, you get one (or more) of these benefits:

1. Increase the amount of money available to all fences in the game.
2. Some of those quests add an additional thieves guild fence to that area.
3. Add another merchant (not a fence) to the Ragged Flagon (guaranteed).

Also, you will need to complete all these special quests before you are given the chance to become the guild master, which has its own set of benefits.

When you complete 5 quests in a specific city, Delvin will give you a quest specific to that city. For each one you complete, a new shop will open up in the Ratworks.

You must complete all 4 city-specific quests to finish the thieves guild.

This question is strongly related, and more specific information can be found there.

After performing five total Small Jobs in a city, Delvin will offer that city's special job. It may be less time-consuimg to quit jobs in cities in which you have already completed the Special Job. In order to restore the Thieves' Guild to its former glory and assume the title of Guildmaster, you must perform these four special jobs.

http://elderscrolls.wikia.com/wiki/Thieves_Guild_(Skyrim)#Special_Jobs