A Ligase is an enzyme that can ligate ("glue together") two molecules with a covalent bond, using energy from ATP.

DNA ligase can ligate broken DNA strands, forming covalent phosphodiester bonds.

An example of how a ligase works (with sticky ends):

5'-AGTCTGATCTGACT        GATGCGTATGCTAGTGCT-3'
3'-TCAGACTAGACTGACTACG        CATACGATCACGA-5'
becomes
5'-AGTCTGATCTGACTGATGCGTATGCTAGTGCT-3'
3'-TCAGACTAGACTGACTACGCATACGATCACGA-5'