In general, a checklist is nothing but a list of items, where an action is required in order to achieve a goal. A checklist could be a to-do list, a list of your day-to-day activities, or a list of a developer's tasks.
In the world of testing, a list could contain test cases to verify, a list of tests that need to be executed, and so on. A checklist varies from person to person, developer to developer, or even from organization to organization, but the purpose of a checklist is always to limit the very human behavior of forgetting something.