GOTM = Game of the Month.
Its a competition that exists for more than a decade on this website.
The sites moderators or admins create a map for everyone to download. They tell you what victory type you need to win for the competition. Everyone then has 1 month to play this same map and compete for who can win the fastest.
They do it twice a month now, every first of the month they create a map on emperor-deity and every 15th they create a map on one of the lower difficulties.
With a little luck, the top competetors post what they have done and why they have done it to get their top results.
There are some awesomely good players there. In civ5 i have not yet won one of these GOTMs, but it is my mission to do so
In civ3 we also had SGOTMs (succesion game of the months) In those games we competed with teams of 6 players who each play sets of 10 turns. It turned into a very fierce competition where every tiny move and detail was discussed into oblivion in the team threads before anyone was allowed to make a move. (usually 5-10 pages of discussion before a player would start doing their 10 turn session with everyone contributing with excel sheets etc to analyse all the options) In my view, that was the highest level of (single player) play you can ever imagine in civ and it was very educational both for all the team members as the people who would read those threads.
I find it extremely unfortunate we dont have this in civ5.
(If you click on my name and find posts, you only have to go till page 4-5 to find these GOTMs and see what i talk about) If enough people feel like that should happen again, we should create a lobby to make it happen.