A double-sharp (##) is an accidental for a note that has two sharps. This means the original note is raised by two half-steps. In standard music notation the double-sharp symbol resembles a bold letter "x" but can also appear as ##.
Chords are generally derived from every other note of a scale and some key signatures contain scales with double-sharps. For example, the key of G# contains these notes: G# A# B# C# D# E# F##. So, the chord G#maj7 which contains the 1st, 3rd, 5th and 7th scale degrees of that scale will include the notes G# B# D# and F##.
Why isn't the F## just called a G? Each scale generally needs to have one of each note letter - In the key of G#, for example, we can't have a G and G#, so we call the 7th scale degree an F##.