What it feels like (contents) is the physical act of short term memory (the here-and-now part) of the perception part where you are recalling the best match up bits of your prior experience to the current perception. And the novel bits that don’t match but that you are learning online. This is felt in the episodic portion of the temporal lobe. When I localized this I am putting what is perhaps undue emphasis on this part as the entire brain is engaged in this perception and there numerous mechanisms all engaged at the same time - the the temporal/EC/HC part is what registers the attention focused digested version of your perception as your experience. You feel and form the memory all at the same time. Part of what you are feeling/'remembering is the loop of consciousness that I have described elsewhere in the forum.
This post describes the mechanism that builds this feeling in detail. Note that pure recall (memory) lacks that “reality feel” of the novelty bits as it is not driven by perception. You might describe that perception part in some other way but there is clearly something missing when you remember an episode vs. going through it.