The usual answer to the question : De quelle couleur est ton manteau ? is: Il (mon manteau) est beige.

Consider it would be the same in English:
What colour is your coat? → It ‘s beige.

What you wanted to answer using a (3rd person of avoir): Mon manteau a une couleur beige would not sound idiomatic at all and we never say that in French. And mind the word order.

If you really wanted to mention the word couleur in your answer, you could have gone with: Mon manteau est de couleur beige, which is not usual but possible, and slightly clumsy unless in a very specific context.

We do not repeat the word couleur in the answer because it is considered as part of the question phrase, and you don’t always have the question word or phrase in the answer (it’s the same in lots of languages).

Quel temps fait-il ? → Il pleut.
Quelle est sa nationalité ? → Elle (il) est français(e).

But it is not always the case, you’ll probably soon learn (if you haven’t yet) quelle heure est-il ?, to which a French person would answer: Il est 3 heures, keeping the word heures in the answer.

Mon manteau a beige couleur is not correct because a is a form of avoir , not of être. French uses the same verb as English in this sentence : The coat is beige = Le manteau est beige , or with the pronoun : Il est beige. Translating the subject it depends of the gender of the noun in French: le manteau is masculine => il ; la chemise is feminine => elle.

You need to understand that in French, like many other languages, objects are not automatically neutral (‘it’) as in English, but female (‘she’) or male (‘he’).
You will need to learn for every noun which of the two it is; this is quite an effort for native english speakers.

In your example, manteau is male, so it gets the french ‘il’.

The crux of your question is in the sentence:

From what I understood, Il est means He is. But, Why does it mean It is?

The fact is that in French there is no “it”. The only French grammatical genders are masculine (applied to male people and animals, and to part of inanimate objects, such as le manteau, il) or feminine (for female people and animals, and the rest of inanimate objects, such as la chaise, elle).

So, for every French noun you have to learn its gender, masculine or feminine, and agree adjectives and pronouns consequently.

French speaker here. It simply means “It is”.

When you wrote “Mon manteau a beige couleur.”, it is the same as saying “My coat has color beige”. You could say instead “Mon manteau est de couleur beige.” which could be translated to “My coat is of beige color”.