If you lawn is prone to drying out in spots, a layer of peat moss as a top dressing can help to retain moisture. Peat moss acts like a sponge, imbibing water. Lawn grass that is in contact with the moistened peat moss can absorb some of that stored moisture.
If your lawn is in a heavy soil, the addition organic matter can help to improve it. A layer of peat moss thinly spread over an existing lawn will help to improve the soil structure, resulting in a healthier lawn.
Peat moss should not be used when establishing new lawns. The peat moss will out-compete new seed for moisture. Unlike straw, peat moss will not decompose, and will create a barrier through which the seed may not be able break.