A mulching mower or recycling mower is one which has the option to finely chop or mulch the grass so that it is small enough to drop down in between the blades of grass. A mulching mower has a specially designed blade and deck which keeps long blades of grass in the cutting chamber for longer so the blade cuts the grass many times until it is small enough to go back into the lawn.
Mulching is not the same as simply not collecting your grass clippings like you could with any other mower. If you did this the clippings may cause harm to your grass by blocking the light and other elements because they are too large.
When you cut your grass you should cut no more than one third of the total length of the grass blade off. If you remove a third of the blade you also remove a third of the water and nutrients in the grass. If you can mulch the grass up into tiny pieces and get it back down to the soil it can help keep moisture and nutrients in your lawn rather than taking them away.