This link has a discussion of what ip redirects are.
http://www.cisco.com/en/US/tech/tk365/technologies_tech_note09186a0080094702.shtml
Now when you should turn them off is more of security thing. In theory they can be used for man in the middle attacks but the ones the router itself sends are not a problem. It is more that some people do not want to see any.
Now because of this possible security issue many of the TCPIP stacks on end user machines ignore icmp redirect messages. In these cases you are just wasting bandwidth sending them since they are ignored.
Unless you feel you have a issue they more than likely do more good than harm. In the most simple setup where there is only a single exit point from a subnet they will never be send anyway.