How does a password manager like keepass key file be used to increase the security?

In addition to acting as "something you have", the option to use a KeePass Key File allows for more flexibility in the other two factors ("something you know" and "something you are") without having to explicitly implement such behaviour in the application.

Example 1: "Something you know" could be run through a custom or stronger key derivation function than KeePass (especially v1.x compatible) can support; then loaded in as a keyfile.
Example 2: "Something you are" could be run through a biometric scanner that writes out a biosignature which is then run through a trapdoor function and/or key derivation function to be loaded into KeePass which has no native awareness of biometrics, especially on operating systems with no "TWAIN" equivalent biometric standard.
Example 3: "Something you are" in the more generic sense of prove you are a human* by regenerating the keyfile (or one stage thereof) from a human typing in a CAPTCHA image (or one or another possible successors) stored publicly along with the keystore.
Basically, the keyfile option can act as a generic catch-all for any entropy source you can imagine - within the limit of the underlying keystore encryption scheme (256 bit for KeePass).