Both are classes of long-term memory. Explicit memory, also referred to as episodic memory, is conscious memory (i.e., the conscious recollection and recall of information previously learnt). Implicit memory is unconscious memory (i.e., memory that does not require the conscious or intentional recognition of information previously learnt). Amnesic patients typically perform normally on tasks involving implicit memory, but poorly on those requiring explicit memory.
See Declarative and procedural memory, Episodic event and semantic memory, Follow-back studies, Memory, Recall memory