For the purpose of this article a rig is what is used to amplify the sound. Some might include pedals as part of a rig but not everyone uses pedals.
There are really 3 things a rig is used for in live performance:
What individuals use their rigs for depends on circumstances.
Many bass players like to have their recorded sound coming from their rig as they feel it is an essential ingredient to their sound. Most recording engineers will not want to mic a rig up; but if you insist they will suggest you give them a DI as well, and pretend to use the mic's while using the DI.
There are pro's and con's for both and there are lots of combo's available with outputs that match a stack.
Dont!