Historically, cavalry have been soldiers who fought while riding horses. In modern times, "cavalry" means the fast branch of the military, as opposed to the slower infantry (soldiers on foot).

An Eastern Han glazed ceramic statue of a horse with bridle and halter headgear, from Sichuan, late 2nd century to early 3rd century AD

Soldiers have fought on horses ever since people have ridden horses. Because horses are strong, cavalry members can wear more armour than infantry and carry heavier weapons. Because horses are fast, cavalry members can ride into battle more quickly than infantry members.

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Cavalry Facts for Kids. Kiddle Encyclopedia.