What's this hazing and how do I fix it?

[Raymond Ho]

I came across an old hope chest.. Sanded it down to the veneer and thought I noticed some horizontal banding / hazing. Stupid me thought hmm maybe a varnish will make this better? It did not.

What caused this?

How would one go about fixing this, short of going back in time?

Please help this newbie here finish learning his lesson. Insults welcome. :D