Usually the t-statistic is used in regression to test whether the regression coefficient (the slope of the line --> b) is significantly different from 0.

If it is, then you have a statistically significant relationship between the two variables --> i.e., if you know the value of one variable, you can generally make reasonable predictions on the other.

The "critical values" are the values that t must equal or exceed in order to be "significant" in a statistical sense - far enough away from 0 to conclude that the difference from 0 is probably not due to random chance.

So for your example, t = 1.518 which is not quite large enough to be significant because the critical values are 1.662 and 1.986. A one-tail test checks to see if t is large enough in the positive direction, and a two-tail test checks to see if t is far enough from 0 in either direction.

Not to complicate things, but the t-test can also be used to check the significance of the correlation coefficient (r) as well.

Hyperstat does a good job of talking about these concepts:

http://davidmlane.com/hyperstat/B134689.html