As two examples: Partial trust means you trust a key for different purposes, or for different levels of validity.
Different purposes: "Do I trust that this key correctly identifies this person?" is a separate question from "Do I trust this person to do proper verification before signing others' keys?" (i.e., trusted link in the Web of Trust)
Different validity: "I've met this person and verified they own the key", is different from, "They've identified themselves with two forms of government ID", is different from "I've known them all my life".
Different purposes: "Do I trust that this key correctly identifies this person?" is a separate question from "Do I trust this person to do proper verification before signing others' keys?" (i.e., trusted link in the Web of Trust)
Different validity: "I've met this person and verified they own the key", is different from, "They've identified themselves with two forms of government ID", is different from "I've known them all my life".