Primarily means mainly or most importantly. When something happens primarily for one reason, that's the biggest reason even if other reasons exist. If you study primarily in the morning, that's when you do most of your studying, though you might study at other times too.

A koala's diet consists primarily of eucalyptus leaves: that's almost all they eat, with only tiny amounts of other foods. A soccer team might win primarily because of excellent defense, even though good offense helped too. When a scientist says a problem occurs primarily in cold climates, she means that's where it happens most.

The word helps you identify what matters most when multiple factors are involved. If you're tired primarily from staying up late, that's the main cause, whether or not playing video games all afternoon also contributed. When your teacher says the essay grade depends primarily on clear arguments, she's telling you that's the most important element, even though spelling and grammar count too.

Using primarily acknowledges that other factors exist while pointing clearly to the dominant one. It's more precise than saying “only” (which would ignore everything else) and stronger than saying “partly” (which wouldn't show what matters most).