There is an X-Wing when, in two rows, a number can only go in two cells of each, and those cells are in the same two columns. The four cells are the corners of a rectangle. The number goes in two opposite corners (you don't know yet which), but either way it takes up both columns. So it is removed from the notes of the other cells in those columns.
The name comes from the shape: the diagonals between the corners draw an X. It works with rows and columns swapped too: a number that, in two columns, only fits in the same two rows is removed from the rest of those rows.
An example
There are no singles, locked candidates or subsets in this grid. Let's look at the 1. In row 5 it can only go in two cells, in columns 1 and 9. In row 9 too: the empty cell in column 6 doesn't have the 1 in its notes, which leaves columns 1 and 9.
The four cells are the corners of a rectangle. The 1 of row 5 is in one of the top corners; the one of row 9, in one of the bottom ones.
There are only two ways to arrange them. If the 1 of row 5 goes in column 1, the one of row 9 goes in column 9. If it goes in column 9, the one of row 9 goes in column 1. Either way, columns 1 and 9 each get a 1 in one of these corners.
A column has only one 1. So the 1 is removed from the notes of the other cells in both columns: from rows 2 and 6 in column 1, and from rows 1 and 7 in column 9.
In box 3, the 1 could go in two cells: the one in row 1, column 9, and the one in row 2, column 8. Without the first, it is left with a single place: a hidden single. And the cell in row 1, column 9 is left with only the 7, a naked single.
Neither row, on its own, tells you where the 1 goes. It is the combination of the two that locks it in the two columns. That is the new idea in the X-Wing: putting together two parallel rows that, on their own, let you conclude nothing.
What is not an X-Wing
Two rows with the number in two cells, but in different columns. Columns 1 and 9 in one, columns 1 and 8 in the other: there is no rectangle, and nothing is locked.
A row where the number fits in three cells. If, in row 9, the 1 could also go in column 6, it would no longer have to be in columns 1 and 9.
How to search
One number at a time. Go through the rows and mark those where the number has only two possible cells.
Look for two with the same columns. If there are, the four cells are an X-Wing.
Do the same with the columns, looking for two where the number only fits in the same two rows.
Check whether it removes anything. The X-Wing only lets you remove candidates if the number is still in the notes of other cells in the rectangle's columns (or rows).
After removing, look for singles, especially in the boxes those columns cross.
Your turn
Find an X-Wing and cross out the candidates removed from the other cells of its two columns (or its two rows). Tap each cell, choose the number and, at the end, press «Check».