A comparison is a formula that answers yes or no. Excel shows the answer as TRUE or FALSE:
=B2>C2 is TRUE when B2 is bigger than C2.
=B2=C2 checks that two cells match; =B2<>C2 checks that they differ.
>= and <= include the boundary: =B2>=100 is TRUE for exactly 100.
Text comparisons ignore case, so ="north"="North" is TRUE. A number and the same digits stored as text aren't equal: Excel treats them as different kinds of value.
IF, AND and OR all work with these TRUE and FALSE answers, so get the test right on its own first. TRUE also counts as 1 in arithmetic, so you can add up matches.