In this video the concept of a function is explained, including its domain, range, and graph. The domain is the set of values in the initial space that can be input into the function, while the range is the set of possible output values in the final space. A key rule of functions is that each input value can only correspond to one output value. An example of a function is the square root of x, which has a domain of all positive real numbers and a range of all non-negative real numbers. The video also discusses different forms of functions, including explicit, implicit, and tabular forms.