Autophosphorylation is a type of post-translational modification of proteins. It is generally defined as the phosphorylation of the kinase by itself. In eukaryotes, this process occurs by the addition of a phosphate group to serine, threonine or tyrosine residues within protein kinases, normally to regulate the catalytic activity. Autophosphorylation may occur when a kinases' own active site catalyzes the phosphorylation reaction (cis autophosphorylation), or when another kinase of the same type provides the active site that carries out the chemistry (trans autophosphorylation). The latter often occurs when kinase molecules dimerize. In general, the phosphate groups introduced are gamma phosphates from nucleoside triphosphates, most commonly ATP.

Reference
Wiki: Autophosphorylation