Equalizer

In category theory, an equalizer of two morphisms $f,g:a{\to }_{\mathcal{C}}b$ is a morphism $h:c\to a$ such that $f\circ h=g\circ h$.

This is exactly a limit of the diagram,

\usepackage{tikz-cd}
\begin{document}
\begin{tikzcd}
a \arrow[bend left]{r}{f} \arrow[bend right]{r}[swap]{g} & b
\end{tikzcd}
\end{document}

Interpretation

In Set, it can be interpreted as the solution in $X$ to a the equation given by $fx=gx$.