Expression Sigils determine the form of the spell, i.e. whether it is cast on a single target, an area, in a line, in a cone, on your weapon or armor, etc.
Expression Sigils also determine what beneficial spells can stack with one another. For example, the Gift of the Golem spell (Guarded Form expression) will stack with Titan's Touch (Focused Intent expression) and Spectral Blur (Focused Intent expression) will stack with Mirror Image (Guarded Form expression). But Titan's Touch will not stack with Spectral Blur as they both use the expression Focused Intent.