Step 1: Recall why atoms bond at all.
Atoms bond to reach a stable, filled outer shell, usually eight electrons, matching the nearest noble gas.
Step 2: Compare the two ways to fill that shell.
One way is to fully give away or take electrons, that forms an ionic bond between a metal and a non-metal. The other way is for two atoms to share a pair of electrons between them so both get to count those shared electrons toward their own outer shell.
Step 3: Match this sharing idea to the question.
The question specifically describes atoms sharing electrons, not transferring them, so this fits the second mechanism. For example, in $H_2$, each hydrogen shares its one electron: \[ H\cdot + \cdot H \to H{-}H \] Both atoms now effectively have a filled shell around the shared pair.
Step 4: Conclude.
A bond formed by sharing electrons between two atoms is a covalent bond. \[ \boxed{\text{Covalent bond}} \]