You really don't want to hear this (tho the source was sketchy...) On our last trailer, the floor looked just like yours. When we traded it in, the salesman said it was from mold and it discolored from underneath. He did say this after we had done the deal, so there really wasn't any incentive for him to say that except to maybe make us feel better for buying a trailer from him. It most likely was mold since every seam on the thing was bad and it seemed to leak even on humid days!
With that said, it might make sense to pull it up and make sure everything underneath is sound.
2007 Surveyor SV291
2005 Durango Hemi