The Gap Interpretation of Genesis 1 holds that the timeline offered to us in Genesis 1 is meant to be taken literally and sequentially but that there are gaps in it.
One version of the theory holds that there is a gap between Genesis 1:1 and the creation of light in 1:3. As this is usually articulated, God first created the world and then it fell into a state of disrepair somehow (possibly by the fall of the angels) so that it became "formless and void" and God then set about a cosmic renovation project, which is what the six days record.
Advocates of this view appeal to certain words in the Hebrew of Genesis 1 that maybe could be translated in a way that would allow for this theory (but not require it) and to certain other passages in the Old Testament whose support for this theory is highly contestible.
These are just scraps though, not solid evidence for the theory.
The Gap Interpretation simply does not leap off the page as a plausible interpretation when you read this text. I am not aware of anyone in the ancient world who proposed it, and it has every appearance of being a desperate expedient to square Genesis 1 with the findings of modern science rather than a plausible interpretation of the text in its own right.
(It’s also not clear how well it accomplishes its intended task, since modern science does not view the current world order as having been re-established/created in a period of six days following a cataclysm of some kind. To try to deal with this problem, some have suggested additional gaps between the six days, so that they represent six individual days–scattered throughout billions of years–on which God did things, but this also is in no way suggested by the text.)
We’ve also still got the Fourth Day sun problem. (And we may have the land-animals-before-birds problem if you go for a gap of millions of years between Day Five and Day Six.)
While one could postulate that there was a space of time before God initiated the day/night cycle on Day One without doing unjust violence to the text, positing that there was a prior creation that deteriorated and that Genesis 1 is simply the story of how THIS PHASE of cosmic history got started is NOT a plausible reading.
The reason is that it mistakes the primary function of the Genesis 1 narrative. It’s a creation story, not a re-creation story. If it were meant to be the latter then the author would have needed to signal this fact in some clearer way than he did. On its face, the commonsense interpretation of the chapter is that Genesis 1 tells us the story of how God established THE WORLD, not just this phase of the world’s history.
So, again, the kindest thing I can say about this is that it is an interesting stab at interpretation but that it is so speculative that it is completely without support–or substantial support, at any rate.
