If you mop up a liquid, you clean it with a cloth so that the liquid is absorbed. A waiter mopped up the mess as best he could When the washing machine spurts out water at least we can mop it up Michael mopped up quickly with his napkin
If you mop up something that you think is undesirable or dangerous, you remove it or deal with it so that it is no longer a problem. The infantry divisions mopped up remaining centres of resistance
The process of extinguishing remaining hot spots insuring the fire will not re-ignite or continue to spread
Once a fire is controlled, Mop-up begins This is the process of making sure all remaining hot spots within the fire's perimeter are completely out See cold-trailing
To make a fire safe or reduce residual smoke after the fire has been controlled by extinguishing or removing burning material along or near the control line, felling snags, or moving logs so they won't roll downhill