Regression testing is applying the previously failed and all the related tests on the modified built.

Eg. Let us suppose there are 25 test cases for the functionality. During the initial testing, the test case numbers 11 and 12 have failed and we can't continue testing unless the 2 bugs are resolved. In such case we first report the bugs. Once we receive the modified build from the developers, we apply previously failed test cases (i.e. 11 & 12) and all related test cases according to the bug (say 6, 7, 8 and 9). After that we continue applying the remaining test cases (i.e. 13 to 25).