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)