Here is a picture of an X-Wing:

The red lines connect 2's that are strongly linked... they are the only possibilities for 2 in rows 4 and 8. The possible ways that those two can be in the solution are marked, one in red and the other in blue(2's written in blue cells). Both possibilities lead to the elimination of the Twos in the red boxes marked with a red X's.

This can be extended to more than 2 rows(or columns). Here is a Swordfish, which is the same concept only has more cells.

Swordfish:

In the picture above, the possibilities are again marked with read and blue 2's. and the 2's in the boxes marked with red X's can be eliminated.

Basically you find possible cells for a particular number in a row (or column )and you have to find the same possible cells(some can be filled with other numbers) in more rows(or columns) and then you eliminate what ever line up with those cells along the columns(or rows)-notice the switch here.

These concepts can be extended to 4 or more rows/columns and they call the squirmbags or squirmfishes or octopi or something... 'higher fishes'. I think there are example of x-cycles.

I hope that helps.