What does an accidental and a sharp mean when they are both placed together next to the same note?

There is no ‘accidental’ mark. What mark are you seeing? The sharp notation is showing that the note is an exception to the rule shown in the key signature.

You can have a double sharp.. and that has a special notation….

Oh.. here, this is a good wiki thing… http://en.wikipedia.org/wiki/Accidental_(music)

As @cazzie said, an accidental isn’t something that has a particular mark. An accidental is just a sharp or flat or natural placed on the staff that differs from the key signature. So a sharp next to a note is an accidental, but I’m not sure what you mean by a sharp and an accidental placed together.

Since what you’re asking doesn’t make sense, could you provide a picture of what you’re talking about? If we could see what you’re looking at, we could tell you what it means.

A sharp is a type of accidental.

There are three major ones: Flat (b), Natural, and Sharp (#), and the not as common Double Flats (bb) and Double sharps (x)

You won’t see much else besides those, especially on a single note.