What is a discriminant as used in math?

For a quadratic equation in the form
ax^2 + bx + c = 0
the discriminant D is found by this formula
D = b^2 - 4ac

It's useful to determine how many and what type of solutions we have for x
If D > 0, then we have two different real number solutions
If D = 0, then we have exactly one real number solution
If D < 0, then we have no real solutions (if you learned about complex or imaginary numbers, then you would say you had two complex or imaginary solutions)