After uploading your code or after periods of inactivity your Lambda is shut down or "cold". When a new event comes in there is a brief moment where Lambda spins up a new instance of your code - this includes whatever initializing AWS does to start up the "container" as well as initializing the code that you uploaded.
So an event that is able to hit an initialized("hot") Lambda will in theory be processed faster than hitting a cold one. There isn't a guarantee on how long a Lambda will stay hot after the last event but it could be as long as 5 minutes.