This looks like a trailing form of moss, and it grows where a lawn is poorly drained and poorly maintained. Carry out remedial works this autumn in the form of scarification, aeration, and application of an autumn/winter lawn treatment which includes a mosskiller. If the area where it grows is shady, it will be difficult to get rid of. Applying a proper top dressing in autumn also helps, specially if your soil is light or sandy. Get yourself a copy of The Lawn Expert by D. G. Hessayon if you want a step by step guide as to what to do, its not an expensive book but it is very useful.