There has been a bit of confusion on what exactly LFR (Looking for Raid) is, so let me explain a bit. LFR or raid finder is a function within WoW that allows you to enter into many of the different raids within WoW with people who you are randomly thrown together with. At the bottom of your screen is what looks like a green eye. If you click this it will bring up a window through which you are able to choose if you would like to que up for a dungeon, raid, scenario, or for flex raiding and looks like:
While there is another way of going about queing for a raid group, this is the most common one. The groups are set at 25 people, with 2 being tanks, 6 healers, and the rest dps (damage dealers). The people that you will be raiding with are a one time deal, unless you que with a friend or happen to get thrown in with someone from your server. There are multiple servers from which these 25 people are pulled from, so the chances of being in a raid with them again are slim.
The other possible way of getting into a LFR is by hitting the O button when you are in WoW, clicking the raid tab at the bottom of the pop up box, and then the other raid tab at the top. You can then both look at those who are qued in this fashion as well as put yourself in que.
For more information about LFR please go to: Looking_For_Raid
I hope this helps a bit! If you have any other questions or comments please feel free to contact me.