Popularized by Japanese giant robot type shows, the term literally refers to the act of merging two seperate entities. It is often interchangable with similiar terms such as fusion, combination, joining, etc.
(i.e. Shinkon Gattai Godannar roughly translates to God soul(Shinkon) Merged(Gattai) Godannar)
Godannar is about to perform its gattai(fusion) sequence.