The applet on this page is designed to help you understand how to the disciminant helps you when dealing with quadratic equations and expressions.
The general quadratic expression is: ax² + bx + c.
The discriminant is: b² - 4ac
Varying a, b, c changes the curve. As the curve changes, notice how the discriminant changes.

It's a good to idea to keep a = 1 to begin with.
The discriminant helps you in deciding whether or not a quadratic equation has 2, 1 or no solutions. Working out the discriminant is also half-way to solving the equation, since the quadratic formula includes the discriminant.
Investigate and learn. Enjoy.