Communicating with the engineer and other artists. Generally overseeing all phases of the project. Some producers do all of these things. Others only one or two. By now it should be obvious that this is not the right question.
Every album has a producer.
In my experience working with artists in the early stages of their career, only a handful have done a good job of producing themselves. If you don't know or can't afford a full-fledged producer, at least have a trusted, knowledgeable friend or colleague critiquing the project as it progresses. In some cases that person can be the engineer, but remember that engineering itself requires their full attention. The recording lacks direction and focus, and fails to bring out the artist's strengths. The musical elements don't go together well, making for difficult, if not impossible, mixes.