Type inference is an algorithm allowing Liberty Eiffel to statically compute (at compile time) the true type of objects at run time.
Usually, this algorithm allows simplifying the generated code by deleting dynamic binding sites when the static type is computed to be reduced to a unique dynamic type. This simplification is summed up and displayed by the compiler when using the -verbose flag. It's called type inference score; it is the fraction of simplified binding sites over the total number of sites.
One should note that a 100% score is usually not possible, nor desirable; else your project is not really written in an OO spirit...