Acceleration in the Kinematics Equations
Concepts:
    Acceleration is the rate of change of the velocity, how much the speed is increasing or decreasing.
    If the acceleration is positive, the object is speeding up and the velocity is increasing.
    If the acceleration is negative, the object is slowing down and the velocity is decreasing.
    If the acceleration is zero, the object's speed is not changing.  It is not slowing down or speeding up, the velocity is not increasing or decreasing.  It is moving at a constant rate.
 

Here's an example of a problem when you could use the kinematics equations.  If a car goes from 0 m/s to 50 m/s in 5 sec, what is the acceleration?
    Use the first kinematics equation.  V=Vo+at
                                                        50m/s = 0m/s + a 5s
                                                        50 = 5a
                                                            a = 10m/s^²
    If you want to know the distance it travels use the second or third.
        x=Vot+1/2at^²
        x=0m/s+1/2 x 10m/s x 5^²s
        x=1/2 x 250
        x=125m

Here's another example.  A car is going 50m/s and comes to a complete stop in 5 seconds.  What is the acceleration?
    Use the first kinematics equation again (V=Vo+at) but this time it will be
                                                                   0m/s = 50m/s + a 5s
                                                                   --50= 5a
                                                                         a=--10m/s^²
    To find the distance traveled you could also use the third equation.
        V^²=Vo^²+2ax
        0^2m/s=50^2m/s+2 x --10m/s^² x X
        0=2500--20X
        20X=2500
        X=125m

If the car is going 500m/s and after 5 seconds it is still moving at 50m/s then
    V=Vo+at
    50m/s=50m/s + a 5s
    0=5a
    a=0

Other pages on this topic:
The Physics Classroom

Acceleration of Freely Falling Bodies
Concepts:
Acceleration due to gravity always = 9.8m/s^2

This means you can always use this as the acceleration when you there is an object in free-fall.  For example say you drop a rock off a building and you want to know its velocity after 3 seconds.  Use the first kinematic   V=Vo+at
                        V=0m/s+9.8m/s^2 x 3s
                        V=29.4m/s
Real-life Applications:
    You can find the velocity, original velocity, acceleration, time or distance of any object as long as you have any of the three out of four values for the variables needed in the equation you use.