Actually, in order to solve the Theorem, You have to look at the diagram:
You can see, Side of Square is (a+b)
So, Area = a * b = (a+b)(a+b)
Now, Area of Smaller square under the square = c²
There are four Triangles, their Area will be: 4(1/2ab) = 2ab
Now, Area under the square will be equivalent to the Total area of Square itself which is the same thing.
So, (a+b)(a+b) = c² + 2ab
a² + 2ab + b² = c² + 2ab
Subtract 2ab from both sides,
a² + b² = c²
[ Hence, Proved ]
Hope this helps!