Regression Testing - When a new code is merge is with 
existing code as a part of Regression testing we are 
ensuring that existing code is mot impacted by the new code.
Retesting - During the execution phase when the defect is 
fixed and tester need to test it again thats known as 
Retesting.

Regression Test:: To check whether the change component
introduce any error in an unchanged component is called
Regression Testing..

Re-Testing:: Testing one module again to check whether its
working fine or not or say second time testing of that
particular test case is called Re-Testing..

Example:: Suppose we have 3 module i.e
Adding,Deleting,Updating now we find some bug in Adding
module and after that bug is fixed we again test that Adding
module is working fine or not this is called Re-Testing and
Testing the Remaining modules to check whether they r
working fine or not after the bug fixed in Adding module is
called Regression Testing..........

Regressin Testing:

Start it in this way:

Suppose you are testing a new release 5.1 which includes 
some more functionality or some previous defects that are 
fixed and incorporate with in this. So what you are doing 
here?

You have your set of test cases for the 5.1 that you need 
to execute first and at the end you have to run your 
regression test cases. WHY?

"This is to ensure that all your functionalities are 
working fine with your current build and also MAKE SURE 
that your PREVIOUS functionalities are not broken"

This is the main motto of regression testing.

Retesting : This means to retest a defect after fixed by 
developers..

More in depth

You got a defect and raise the defect for fix.After the 
defect has been fixed you need to check it whether its 
working fine or not that means you are testing it another 
time to check its behaviour.

This is called retesting.