River deltas are formed by deposition of sediments.
The river deltas appear in the area where the river enters another river, lake, sea, ocean, estuary, which are not able to take away all of the sediments that the rivers is bringing with it.
Because all of the sediments can be taken away by the other bodies of water, the river is depositing the sediments at and around the connection part. As the sediments keep coming, all of the surrounding area will be covered with them, so the river will form a delta because the sediments will be blocking the free flow of its waters, thus it will spread into a triangular shape at its entry.
