Period (T)-  Time it takes for something to happen once.  Also the reciprocal of frequency.  For the frequency example above, since f=2/sec, then the period is 1/2, or .5sec

Displacement (X)- Distance.  The distance moved from some point.  When considering waves and SHM, the displacement is measured from the point where amplitude would be zero.  Due to the nature of SHM, there are + and - values of X.  For example, if a kid rests in a motionless swingset, you could either move them forward in the swing (which we might choose to call positive) or move them backward (which would then be negative)

Amplitude- Gives the amount of energy of a wave.  The greater the amplitude, the more energy.  For example, the maximum amplitude of a mass on a spring is the maximum distance the spring was pulled in one direction.  Note that there are two "maximum" values; +A and -A.  Note: Amplitude and displacement are often used interchangeably, you will see this most often as Xo=A

Acceleration (a)- Force in SHM acts to oppose the motion (to return X to zero) , so the acceleration is negative when displacement is positive, and positive when displacement is negative.

Velocity (v)- Velocity for an object undergoing SHM reaches its maximum when the object crosses the X= zero point (a kid on a swing goes the fastest when the chain is vertical).