Snowblower auger spins easily and does not turn impeller
There are sacrificial bolts (shear pins) that break on purpose if you hit something solid (like a rock). Check for them.
It generally replaces just like a bolt (with a nut on one end, but it might use a cotter pin or similar). But DO NOT USE A BOLT. It needs to be able to shear, so get the right part (they are VERY common - should be no issue). Check the other end of the auger for one that's still intact for a sample.

Here's a close up of the installation of a shear pin/bolt that is designed to break.  Each side of the gearbox will have at least one.  If your snowblower is a three-stage unit, there will be more.


Here's a close-up of a replacement supplied with a Cub Cadet. You can see it uses a clip to install and the notches designed to break are obvious.  They are 1/4&quot; diameter and about 1-1/2&quot; long.  Even though my three-stage snowblower uses four in total, Cub Cadet only gave me three spares.