Determines how group membership lookup is performed.

This option is here because we the Jenkins developers are between a rock and a hard place when it comes to determining groups that an user belongs to. We have several approaches implemented over the time, but none of them seem to satisfy everyone. So we basically threw hands in the air and asking you to find one that works for you.

The only people who should try to tweak this setting is (1) those who find login very slow or (2) those who find that Jenkins isn't picking up all the groups that you belong to. The general rule of thumb is that you try both options while paying attention to the time it takes to login and the groups reported in the "/whoAmI" page, and pick one that works for you.

Automatic
Do the best to pick the "best" algorithm. Specifically, Jenkins tries LDAP_MATCHING_RULE_IN_CHAIN first, and if it's going too slow, then stick to the "recursive queries".
Recursive queries
For each group X that Jenkins discovers, recursively list up all the other groups that has X as a member, by issuing a separate LDAP query. This increases the number of queries, but each query remains simple. Note that several people reported that this approach fails to find some groups that the user is actually a member of, but the developers of this plugin do not have access to such AD deployment to investigate the claim.
LDAP_MATCHING_RULE_IN_CHAIN
Use Microsoft extension to LDAP that was specifically added to Windows 2003 to perform recursive group membership lookup. The general consensus in the developer community appears to be that this is the way to go, but several Jenkins users have reported that this approach makes lookup intolerably slow.

It is less than ideal to ask users to make a choice like this. If you have insights to share to improve this situation, or even just data point, please add your thoughts to JENKINS-22830.