Regression testing is testing of a build when the 
bug/defect re-opens.

for eg. a bug is found is build1, it is reported to a 
developer, u execute the same script on build2, if it re-
opens it is nothing but regression testing.

When we talk about manually performsing regression 
testing ,its nothing but executing the same test case on 
various builds and it should be the same when it comes to 
automation too as regression testing is a main candidate 
for regression testing.

"Regression testing is testing of a build when the 
bug/defect re-opens"
The above statement is wrong, Regression testing is a series
of tests run on a build whenever any code has changed in the
existing code, and not necessarily just when a bug/defect
re-opens.

regression testing is, performing the test repeatedly to 
find if the solution to the reported bug have not inserted 
any other bugs or side effects in the application . where 
as the above mentioned ans seem to be ans for re-testing

Regression Testing is testing a new version of an existing 
application/software for bugs that might be introduced 
while adding fucntionality or extra features into the 
application/software.

Usually done after the functional testing is completed. 
Mostly achieved by executing the negative test cases of the 
previous build/version.

Regression Testing is the process of testing the existing 
application with the new functionlities/Modifications.