\lefteqn{eqn}prints eqn in display math style, but pretends that it has zero width. It is typicaly used within an Eqnarray environment for displaying long equations that require multiple lines.
A typical use might be
\begin{eqnarray} \lefteqn{\int_0^\infty some expression =} \\ & & some terms \\ & & \mbox{} + more terms \end{eqnarray}Note that the empty \mbox{} is so LaTeX knows that the following + is a binary operator, and is not attached to the first of the "more terms" as a unary operator.