The area where a river meets an ocean and contains a mixture of fresh water and salt water?

Short answer:

When fresh water meets salt water and they mix, the result is brackish water. (See related questions.)

An estuary may be formed when this occurs at the mouth of a river. (See related link.)

More:

An estuary is a partially enclosed area where a fresh water source such as a river flows into a salt water body such as a sea or ocean. The area is termed an estuary if both ocean and salt water influxes substantially determine the nature of the body of water, hence it would normally be partially enclosed and retaining a significant portion of fresh water influx that is not immediately diluted into the seawater.

Estuaries are often both interesting biological systems and interesting geological formations.

Note: For the more general question of where fresh and salt water meet, see related questions.

Note: If one is interested in the halocline, which is a strong vertical gradient of salt concentration form sometimes at the interface of fresh water and salt water, then that is a different question.