A basis point is 1/100th of a percentage point. In your example above the Eurorate change was from 1.55% to 1.5%.
If you want to know how monetary policy is set in the Eurozone you can go to here to start your research.
If you want to know about monetary policy in general, and a bit about the mathematical underpinnings, there is a wikipedia entry that can start you off. A doo run-run-run, a doo run-run
