In the early days, when Rome was still a kingdom the population was subdivided according to wealth and this subdivision was used not only for taxation purposes but also in order to make up the various military orders.
The equestrian order “Eques”, “Equites”, “Equestri” or “Equestris ordinis” included the knights or cavalry. It was rather like a club to which you might belong according to your personal wealth. The Equestrian rank essentially meant you you had an estate of at least 400 Sestertia. In later years belonging to the equestrian rank gave the right to a horse at public expense whilst on military campaign.
The Equestrians outnumbered the Senators and had a set of privileges although these were not quite as extensive as those of the Senatorial class. An Eques could in any case aspire to reaching the Senatorial order (by getting sufficiently rich). The privileges of the Equestrians were also used to distinguish oneself from those of lower social rank.
Amongst the privileges of the Equestrians was the right to a “clavus” on the tunic (a purple stripe down the tunic but thinner than that of a Senator) and a distinctive gold ring. The Eques had right to particular seating at public games as well as having a degree of legal privilege.
It is an interesting anecdote that it was not unheard of for non-equestrians to try to fake their rank by wearing fake gold rings and clothing of that rank in order to impress or simply to gain access to privileged seating at the games.
At various times of the empire it was not unknown for Equestrians of failing fortunes to try their luck at rich and fame by joining in the Gladiatorial shows as privateers ie not operating under the tutorship of a “Lanista“. This was generally viewed as being against public dignity and there were various times when the sheer number of them brought the authorities to make laws to limit their participation.