A nick is a break in one strand of a DNA sugar-phosphate backbone when the nucleotides on both sides of the break are still present and aligned within a duplex.

The enzyme DNA ligase seals such a break by forming the missing phosphodiester bond between an adjacent $3'$ hydroxyl and $5'$ phosphate.

Schematically:

... DNA — 3′OH   5′P — DNA ...
              ↑ nick

          DNA ligase
              ↓

... DNA — continuous backbone — DNA ...

Ligase seals; it does not fill sequence gaps

This distinction is important.

If one or more nucleotides are missing, DNA ligase cannot infer and synthesize those nucleotides. A DNA polymerase must first fill the gap using a template. Ligase can then seal the final nick left between adjacent DNA segments.

Thus a common repair pattern is

remove damaged DNA
      ↓
gap remains
      ↓ DNA polymerase
gap filled, nick remains
      ↓ DNA ligase
continuous backbone

The same chemistry is reused in different processes

DNA ligase performs the same basic backbone-sealing responsibility in several contexts:

• joining Okazaki fragments during lagging-strand replication;
• completing base- and nucleotide-excision repair after resynthesis;
• sealing DNA ends during several double-strand-break repair pathways;
• laboratory assembly of DNA fragments.

The surrounding proteins and DNA structures differ, but ligase's local chemical job is the same: restore covalent continuity where the correct DNA ends are already positioned next to one another.

Separating gap filling from nick sealing makes DNA-repair mechanisms easier to reason about: polymerase reconstructs missing sequence information; ligase closes the remaining backbone discontinuity.