Prospective memory is a form of memory that involves remembering to perform a planned action or recall a planned intention at some future point in time. It is a type of planning behavior, and also a form of future-oriented cognitive processes.
There are lots of easy example, such as remembering to get milk on the way home to remembering to attach an email to a message you are currently writing to remembering that next spring you need to make a charitable donation before tax returns are due. People can be both very good and very bad at prospective memory.
There are two basic types - event based PMs, where the intended, stored future action is implemented on the basis of the right context (e.g., stopping to get more windshield washer fluid next time you are near an auto parts store), or time based PMs, where the intended action must be implemented at a specific time (e.g., remembering that you need to call your grandmother next Sunday at exactly 5:00 because she is having her birthday party then).
There is a lot of research into PM looking at a lot of questions. One big issue is the extent to which PM relies on monitoring of some sort (for noticing when it is the right time or the right context to implement the intended action) versus being more spontaneously retrieved (e.g., maybe happening to notice the auto parts store while sitting at a red light, and then remembering you need something from there). This is often studied by examining whether there are costs to ongoing activity performance as a function of intended prospective actions. For example, as the time nears for calling grandma, you might find it harder to concentrate on the book you are currently reading.
Some animal research has been done on PM in animals, largely with rats, primates, and a little bit with pigeons. They do seem to show many of the constituent parts of a PM system.