The cover of an agent is the role that an agent plays to hide that he’s actually a spy. So, when you are “under cover”, you pretend to be someone else, or you act as if you have a different job than being a spy.
To make sure that your “cover” isn’t “blown” (ie. you are discovered to be a spy), the cover should help you explain why you are where you are, and why you do what you do.
To make a cover believable, it is often preferred to use real-life experiences as the basis for your cover story and profile. This makes for a more convincing “legend” when under intense questioning or scrutiny.