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To say: "You are right.", I know that it is also acceptable to write: "Vi estas prava.", which to me makes sense, because then 'prava' is an adjective, just like in English.
However the more common way of saying: "You are right.", is simply: "Vi pravas.". I don't see how that makes any sense. How can "to be right" be a verb?
You are right that prava is an adjective and prav- is an adjective root. Esperanto has the additional grammar feature that any adjective root can also be used as a verb. For example:
Liaj okuloj fajre ruĝas [= estas ruĝaj] pro plorado!
Ĉu vi kontentas [= estas kontenta] pri la kurso?
Fortunati fojfoje lacigas la orelojn, ĉar ĝi iom laŭtas [= estas iom laŭta] kompare kun la fono.
In general Esperanto is a lot more flexible about using words in different roles, such as verbs as nouns and and nouns as adjectives etc, because each role is clearly marked with the appropriate ending and it’s not as confusing as it would be in English.
In a Duolingo post Thomas "Salivanto" Alexander has a list of adjectives that can be verbified. The list is complied by another known esperantists Lee Miller. Pravas is on that list.
The problem is that you can divide adjectives into two groups when it comes to verbifying them:
You cannot change the second group, those verbs must be memorised. Therefore it is a good idea to keep the number of verbified adjectives in the first group as low as possible in order to have less things to be learnt by heart. In other words use only those verbified adjectives that are on that Miller's list, and do not assume that the remaining adjectives can be verbified.
There's probably no definitive answer as to why Esperanto uses a verb for that, just as there's probably none to why English uses an adjective for it. (For why both are possible in Esperanto, see Neil's anser.)
Languages differ in how they express certain concepts. They even differ in what concepts they ascribe to situations. Is "being right" a property (trait) of the person? (That's what adjectives are usually used for.) Or is it related to what they do (e.g. say or write)? (That's what verbs are usually used for, sometimes in combination with adverbs.) It's difficult to give a neutral answer to these question that isn't primed by one's native language or other languages one's familiar with.
While English deemed1 an adjective more fitting for describing that someone states or stated something that's correct, Esperanto favors1 a verb, but also allows for the adjective, if one prefers. (And as Neil noted, the adjective is actually the base form of the word / root prav-.)
And those aren't even the only options: German expresses that notion with "Recht haben" so seemingly applies the concept of possession instead of that of action or trait, and uses a noun together with "haben" ("to have (got)"). French's "avoir raison" also works that way, but French also seems to have "dire vrai" to express more or less the same.
Just like any living language, Esperanto isn't just a copy of another language (e.g. English) with only words substituted. It has not only its own grammar, but also its own idioms and expressions. While Esperanto was designed to be more logical than many ethnic languages, so that it'd be easier to acquire and so one can often deduce the correct phrasing from the wanted semantic and vice versa, there are statements that cannot be made without choosing some concepts to express them, and the choice made in Espranto can seem (and not seldom is) arbitrary when seen from the perspective of other languages.
1 Off course languages don't themselves make decisions. It's the users of the language past and present, and in the case of planned languages, the creators, who collectively consciously or unconsciously made and make those decisions. I'm phrasing this metaphorically / allegorically.
