Ogeima is a Japanese term from the game of Go (Wei Qi/Badouk). It is also known as the "large knight's move" because of its similarity to keima, or the knight's move (which, in turn, is named because it resembles the movement of a knight in chess). It refers to a certain type of move, when a player plays a stone three steps one way and one step orthogonally to another stone of the same colour, with no other stones between. This description is a bit confusing, so hopefully this diagram will make it clearer:

.........
...*.*...
...,,,...
.*,,,,,*.
..,,o,,..
.*,,,,,*.
...,,,...
...*.*...
.........

A move at any of the points marked with an asterisk would be considered to be ogeima from the previously played stone (o). Note that all the points marked with a comma instead of a period must be empty, or else some of the asterisked points would not be ogeima.

Ogeima is a very fast, loose move. It is fairly easy to cut the two stones apart, even in the absence of other stones, so it is not appropriate to play ogeima as a defensive move. The advantage of ogeima is that it expands a player's territory or influence quite quickly, compared to smaller, tighter moves. This makes it very efficient for attacking. It is often a better choice than niken tobi because it is equally fast, and slightly better connected.

Here's an example of using ogeima for attack (edges of the board marked by ###):

#..........
#..o.......
#..........
#..........
#...*......
#..........
#..x.a.....
#..........
#...o......
#..b...o...
#..........
###########

Black (x) has just made an invasion into an area where White (o) is fairly strong. White must attempt to put pressure on the invading stone and build territory while attacking it. There is a proverb that says "Attack from the weaker side." This means the side where you are weaker, since adding a stone on that side will strengthen it while attacking. White decides to follow this proverb and attacks from the top by playing ogeima from her top stone (shown with an asterisk). The most likely responses (at least at my very amateur level) for Black are to make an ikken tobi jump to a, or dive into the corner with b. Both will result in White making secure territory while Black fights for his life.