Tilting refers to a change of measure of the form $e^{\lambda \cdot x}/C(\lambda)$ where $C(\lambda)=E(e^{\lambda\cdot X})$.
(The setup is that the measure for which you are proving large deviations is a topological vector space $X$, and $\lambda$ is in the dual space to $X$). The name tilting comes because the effect of the change of measure translates to modifying the ``typical behavior'' under the tilted measure; more technically, the tilting adds a linear term to the log-moment generating function, and that translates to a linear shift in the corresponding Legendre transform that will represent the rate function.