The sum of square C is equal to the sum of square A and B. ( 25 = 9 + 16 )
The Egyptian surveyors, the Chinese and Babylonians knew this rule already about 2000 BC, but they couldn't prove it. The first people we know proved it are the Pythagoreans, it might have been Pythagoras himself. Thereby they raised the rule to the status of a theorem.
The theorem is important to the evolution of the Greek concept of number and the proof demonstrates how the Greeks used such proofs.
Pythagoras theorem can also be used for triangles that aren't right. Then it goes:
c" = a" + b" - 2ab
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