An associate producer is a high ranking member of the production staff who is generally subordinate only to the producer and executive producer, but who also has a set of responsibilities defined by the producer or one of the execs.
In the classic era, the title, "associate producer", was used for only two people: Mervyn Pinfield (from An Unearthly Child to The Romans and again for The Daleks' Master Plan) and Peter Bryant (for The Faceless Ones and The Evil of the Daleks). The exact definitions for Pinfield and Bryant's duties are unknown, but they were likely different from those used by the present production.
Associate producers have been much more common features of BBC Wales productions. In at least the modern sense, there's not a lot of difference between an "associate producer" and a "line producer". Both are responsible for directly assisting the producer with the day-to-day management of production, and are frequently tasked with scheduling and daily fiscal operations.