Magnitude refers to the size or extent of a quantity and can be applied in various real-life situations. Pythagoras' theorem is a mathematical formula used to calculate the magnitude of a line segment in a coordinate system, specifically by forming a right triangle. The formula states that the square of the magnitude equals the sum of the squares of the other two sides. In vector terms, magnitude is essentially an application of Pythagorean theorem principles. The discussion also touches on confusion regarding resultant vectors and their relationship to magnitude, indicating a need for further clarification on these concepts.