This is the term given to a mountain bike with no rear suspension.
Some hard tails have rigid front forks but most have a suspension front fork.
They are light, good value, versatile and suitable for a wide range of riding styles.
You can fit smooth road tyres for commuting, semi slicks for both road and off road, or knobbly tyres for cross country.

“Duallies” or full suspension as they are known, have both front and rear suspension.
This provides more comfort than a hard tail on rough terrain and helps to keep the rear wheel on the ground for more traction.
These bikes come in a wide range of frame and suspension designs and offer varying amounts of suspension “travel” from 3” to 7” to suit the riding you want to do.