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As Leo has already described, L3 switches, like the 3750 series, can "route". (NB: it's this capability that distinguishes L2 vs. L3 switches.)
As Leo also has described, L3 switches often don't have as many features as "routers" and the later 3750 series, the -E and -X models, features are controlled by the installed license. The original series of 3750 features are controlled by the loaded/active IOS image (which requires different "paper" licenses).
Lastly, as Leo has also noted, the lower licensed 3750s might support a basic routing protocol, like RIP, but same also usually support static and local interface routing. I.e. you may not need a routing protocol at all.
