Typically this becomes an issue on larger lawns above about 1/4 of an acre, or if mowing the lawn is simply taking too long.
Essentially mulching mowers recut every blade of grass very finely, and deposit the tiny shavings back into the lawn where they should barely be visible.
Unlike many preconceptions mulching is able to inhibit moss growth, and lead to healthier lawn but you need to follow some basic rules.
Cut regularly and often, generally taking no more than a 1/3rd of the height off the grass at any one time.
Keep blades sharp, and the underside of the deck clean so that the grass can be circulated and recut many times.
Try and leave your grass a bit longer to leave yourself sufficient space to "hide" the clippings. Mulching works best when the grass is cut no lower than 37mm (1.5") to 50mm (2").
The advantages of mulching are:
Up to 30% time saving over an equivalent sized collecting machine because you simply don't have a box to empty.
No unsightly mound of compost at the end of the garden
You don't get covered in grass dragging it out of the grass box to put it on the compost pile.
Healthier lawn, with less need to feed and water because the nutrients are constantly being returned.
If the grass gets too long you may see lots of clumps after it is cut. To remove you may to cut again the next day to disburse them. (Remember though collecting can also be a real chore when the grass gets very long)
Although hidden the cut grass is still there. Because of this it will pick up on your feet, and those of pets and children for up to 24 hours after the grass is cut.
Overall mulching can be a massive benefit although it is not for everyone. In our experience it works best on paddock type areas where you are not looking for the perfect finish, but want a tidy lawn with the least fuss.
Many hay fever sufferers have told us that they prefer mulch mowers because they don't have to handle the cuttings at all.