One square metre is 1.1959900463 square yards. As with the linear pair, the two units are unusually close — about twenty per cent apart in area, against nine per cent in length — and it is the squaring that widens the gap.
About the units
A square yard is the area of a square one yard on a side, and since the yard is exactly 0.9144 metres, the square yard is exactly 0.83612736 m². Nine square feet make a square yard, which is the squared version of three feet to the yard and the relationship people most often get wrong. The square yard's practical role is as a trading unit for soft goods sold by area — carpet, turf, tarpaulin — where the yard was already the standard length measure and squaring it was the obvious next step.
The exact factor
The derivation is 1 ÷ 0.9144² = 1 ÷ 0.83612736 = 1.19599004630108... The nine-per-cent length difference becomes a twenty-per-cent area difference, and the same squaring turns three feet per yard into nine square feet per square yard. That second relationship is worth stating explicitly because it is the classic error: someone dividing square feet by three to reach square yards will overstate by a factor of three, and the resulting figure is plausible enough to make it into an order.
Where you meet this conversion
Carpet and flooring are the main case in the United States, where product is sold by the square yard while rooms are measured in feet — and the conversion between those two is the nine, not the three. Turf and artificial grass follow the same convention. In construction, concrete slab area may be given in square yards while thickness is in inches, requiring both to be brought into the same system before volume can be calculated. Outside those trades the unit is rare, and metric countries use square metres throughout.