I depends on the concentration of the acid.
Hyghly concentrated acid dehydrates the wood and may even char it. This reaction is quite fast (seconds/minutes).
At lower concentration, there is a slow reaction (days), but the wood is partially hydrolyzed, and the cellulose breaks down in the individual sugar molecules. This results in wood, loosing its strong structure. It becomes weak and can easily be broken. It also absorbs water, which is in the acid, but because it looses its structure, it can swell.