In terms of the mean and standard deviation:

-What does it mean to say that a particular value of x has a standard score of +2.1?
-What does it mean to say that a particular value of x has a z-score of -2.4?

There is more than one type of standard score — Z score and T score. The T score = 10Z + 50, but I assume the question is asking for the Z score.

Z = (score-mean)/SD

Essentially, it is telling you how many standard deviations the score is above/below the mean.