The premise is simple:  just like searching for a key word or phrase, you can search for an equation (well, actually any expression, not just equations) written in LaTeX and the search tool will find papers in which that equation occurs. Here’s an example of searching just for $I(G;x)$ which is a commonly used notation for the independence polynomial of a graph.
The trouble is that apart from carefully chosen examples like this one, it just doesn’t work very well. Even ignoring the huge limitation that it only searches Springer articles, it’s difficult to actually search for anything whose precise form you don’t already know. An expression or equation involving a particular mathematical concept can be written in many different ways, simply by minor variations of notation or choice of variable name. For example, the chromatic polynomial of a graph can be written $P(G;\lambda)$ or $P(G,\lambda)$ or $P_G(\lambda)$ or $P_G(z)$ or $P_G(q)$ and so on, and unless you hit on exactly the right one, you’re out of luck. If I’m looking for some dimly remembered equation involving chromatic polynomials, I’d be much better off using MathSciNet and searching for “chromatic polynomial”. Even worse, the exact same expression can be rendered in LaTeX in different ways, depending on which flavour of LaTeX has been used, so you might search hard for $\frac{1}{2}$ only to discover that the author used ${1 \over 2}$.