As there are so many different branches of mathematics, there can be no one definition of the the subject.
In very general terms however, math can be described as the measurement of relations between the forms that we see all around us in reality. Galileo described mathematics as 'the language of the universe' that we had to learn in order to understand life.
What most people think of when they bring to mind mathematics is, strictly speaking, arithmetic; that is, the adding, subtracting, dividing and multiplication of numbers. This developed with the rise of the earliest human civilizations and their need to feed themselves, transport goods and construct roads and buildings.
The Study of Mathematics Began in Ancient Greece
By the time the Ancient Greeks started to look upon math as a science in itself, around 500-600BCE (Pythagoras was one of the earliest of what we could call mathematicians), other branches of math had developed: Geometry (volume and space), needed for major architecture projects, and astronomy; these in turn led to algebra and trigonometry, practiced in Egypt and Babylon. Modern mathematics as we now it began arguably with Isaac Newton and his Philosophiæ Naturalis Principia Mathematica, published in 1687.
To learn more about the history of mathematics, watch this video: