Muggles' Guide to Harry Potter/Magic/Occlumency

Overview
Occlumency is the ability to block one's mind from a Legilimens.

Extended Description
Occlumency is the counter to Legilimency, of which Voldemort is a master. Characters like Severus Snape use Occlumency to hide their intentions. Harry Potter is taught Occlumency lessons in Harry Potter and the Order of the Phoenix. Both Snape and Dumbledore are accomplished Occlumens. Gellert Grindelwald is also an Occlumens. He is able to conceal his mind from Queenie Goldstein, a natural-born Legilimens.

Analysis
It is certain that Harry's ability to block his thoughts from Snape and Voldemort are not being helped by Snape's lessons. Harry's scar seems to prickle constantly after his lessons start, though that may be coincidence; it is at about the time that his Occlumency lessons start that Voldemort becomes aware that Harry can see into his mind on occasion, and it is shortly after that when Voldemort starts actively trying to get Harry into the Ministry. It is entirely possible that Harry's increased reaction may be due to increased probing from Voldemort. However, all through the lessons we see that Harry is unable to prevent Snape from viewing his memories, and at the end of Harry Potter and the Half-Blood Prince, we see that Snape is able to block any of Harry's spells before he can complete it, because of Snape's being able to read his intentions.

Greater Picture
There is some question as to whether Occlumency would even work for Harry against Voldemort. Occlumency is designed to prevent an outside mind from being able to read what is happening within your mind, but as we learn in Harry Potter and the Deathly Hallows, there is actually a fragment of Voldemort's soul within Harry. Does that bit of shared soul provide more access to Harry's mind than simple Legilimency? Harry never finds out, as he is never placed in a position again where he has to try and block Voldemort from his mind.