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In biochemistry, a ligase is an enzyme that can catalyze the joining of two large molecules by forming a new chemical bond, usually with accompanying hydrolysis of a small pendant chemical group on one of the larger molecules or the enzyme catalyzing the linking together of two compounds, e.g., enzymes that catalyze joining of C-O, C-S, C-N, etc.
Like just about every other enzyme that operates on DNA, ligase is fussy about the precise chemistry of the reactions it catalyzes. In the image below, there are two examples of short DNA strands with a break in the background, highlighted by the red circle.