1. It is used as a counter-point to significance tests were it gives an indication of how big or small a significant difference is. This difference can then be compared to Cohen's estimates of what is typical of a small, medium, or large effect.
2. To provide a common metric on which to compare effects for meta-analysis or what not when outcome variables may be measured on different scales.
As an example suppose we found a significant difference in self-esteem in a sample tested before an intervention and then again afterwards. A Cohen's d of .50 would suggest that the intervention program was associated with a half of one standard deviation increase in self-esteem.
and yes it can be used with t-tests.