In a medium to large enterprise, it is highly likely that you will have a dedicated or part-time DBA. The DBA role is particular to each organization; some organizations would give developers and power users access to query execution plans; some would put it squarely in DBA domain. Your DBA will be your last resort after you checked all your application logic (nested loops, recursive functions, memory leaks, and so on), optimized the returned data sets, helped users to clean up computers from CPU hogging adware, and checked your SQL code for Cartesian JOIN(s) and unnecessary functions.
DBAs worth their salt will have intimate knowledge of the RDBMS your application is using. They know what an Oracle extent is and how to use DBCC in SQL Server. They will talk to your network guy, discussing things like double hops, DNS configurations, and excessive network collisions. They will set up traces on the processes running on the server and will help you figure out possible culprits. They will adjust database privileges, check query execution plans, resolve transaction deadlocks, and, if needed, help you with advanced optimization such as query caching and memory pinning.
In short, your DBA is your friend, be nice to her or him, as the case may be.