Consecutive interpreting - interpreting after the speaker has finished talking. While the participants are talking, the intepreter listens and takes notes. When the talking is finished, interpreter retells everything in the target language.
Additional information about the consecutive interpreting you can read here.
Simultaneous intepreting - opposite the consecutive interpreting. The interpreter renders the message in the target-language as quickly as he or she can formulate it from the source language, while the source-language speaker continuously speaks.
Additional information about the simultaneous interpreting you can read here: