To avert is to turn away or to prevent. You might avert your gaze or avert a disaster — either way, you are avoiding something.
The verb avert comes from Latin roots that mean "to turn away from." Averting has that sense of deflecting, turning away, or preventing something (usually bad) from happening. You might put salt on an icy sidewalk to avert accidents, or you might avert a toddler's meltdown by supplying a lollipop.