When material carried by a river reaches the sea, it enters still water. As a result, the material - clay, silt and sand - is dropped. Over time this builds up on the sea bed and reaches the surface to make a delta.
There are two common types of delta. One is called a 'bird's-foot delta', which has many long fingers reaching out into the sea. You get this when a river delta has a few major channels on it. The Mississippi has a delta of this kind. The other kind is a 'fan delta' like the Nile shown above, and is produced when the river splits up into many small channels as it reaches the sea.
Deltas are normally very fertile, and they have been the places where many civilisations have grown up.