Ez a világ legjobb műhelye.

Because Hungarian normally omits van (to be) in the present tense, third person, when one noun phrase is identified with another.

So:

Ez a világ legjobb műhelye.
literally = This the world's best workshop.
natural English = This is the world's best workshop.

You would use van in other kinds of sentences, for example for location/existence or in other tenses:

• Itt van. = It is here.
• Ez a világ legjobb műhelye volt. = This was the world's best workshop.

Not in this sentence.

That is a very common first impression, because in Hungarian ez a often does mean this + noun, as in:

• ez a könyv = this book
• ez a műhely = this workshop

But here the sentence is structured like this:

Ez | a világ legjobb műhelye
This | the world's best workshop

So Ez stands alone as this, and the next a is simply the definite article starting the phrase a világ...

Because a is the definite article, meaning the.

So:

• a világ = the world

In this sentence, a világ legjobb műhelye means literally the world’s best workshop.

Hungarian uses articles quite regularly with nouns, including inside possessive phrases like this one.

Műhely means workshop.

Műhelye is the possessed form: his/her/its workshop or X’s workshop, depending on context.

Here it means:

• a világ műhelye = the world’s workshop

So the -e shows that the noun is possessed.

This is very typical in Hungarian: possession is marked on the possessed noun itself.

Hungarian often expresses possession with this pattern:

possessor + possessed noun with possessive ending

For example:

• Péter könyve = Peter’s book
• a város központja = the city’s center
• a világ legjobb műhelye = the world’s best workshop

So instead of using an English-style apostrophe, Hungarian usually puts a possessive suffix on the second noun:

• műhely → műhelye

The possessor here is a világ (the world), and the possessed thing is legjobb műhelye (best workshop).

Yes.

By itself, műhelye can mean:

• his workshop
• her workshop
• its workshop

But if the possessor is named in the sentence, then the meaning comes from that:

• a világ műhelye = the world’s workshop
• Péter műhelye = Peter’s workshop

So in your sentence, műhelye is not vague, because a világ tells you who or what the possessor is.

Legjobb means best.

It comes from:

• jó = good
• jobb = better
• legjobb = best

So the superlative is formed with leg-, but this adjective is irregular because jó becomes jobb, not jóbb.

This is one of the most important adjective patterns to learn:

• szép = beautiful
• szebb = more beautiful
• legszebb = most beautiful

But:

• jó
• jobb
• legjobb

Because Hungarian adjectives usually do not agree with nouns the way adjectives do in many Indo-European languages.

There is:

• no grammatical gender agreement
• usually no plural agreement in this position
• no special adjective ending here

So:

• jó műhely = good workshop
• jobb műhely = better workshop
• legjobb műhely = best workshop

The noun carries the important marking, not the adjective.

The neutral structure is:

Ez | a világ legjobb műhelye.
This | the world’s best workshop.

Because the copula is omitted, the sentence is essentially:

• subject/pointer: Ez
• predicate noun phrase: a világ legjobb műhelye

Hungarian word order is flexible, but changing it changes emphasis. For example:

• A világ legjobb műhelye ez. puts more focus on this as the thing being identified.

So the given order is a very natural neutral way to say it.

Yes. A very common alternative is:

Ez a legjobb műhely a világon.

That means literally This is the best workshop in the world.

So Hungarian has at least two natural patterns here:

• a világ legjobb műhelye = the world’s best workshop
• a legjobb műhely a világon = the best workshop in the world

They are very close in meaning. Your sentence uses the possessive-style version.

Usually műhely means workshop, atelier, or studio: a place where work is made, repaired, or practiced.

Depending on context, it can refer to:

• a craft workshop
• an auto repair workshop
• an artist’s studio
• even a figurative creative workshop or professional circle

It is not usually the normal word for a store/shop where things are sold. For that, Hungarian more often uses bolt.

So műhely is about a place of work or making, not mainly a retail shop.

Yes. Hungarian also has a more explicit possessive pattern with -nak/-nek on the possessor:

• a világnak a legjobb műhelye

This also means the world’s best workshop.

Compared with a világ legjobb műhelye, the -nak/-nek version is more explicit and can sound more marked depending on context. The version in your sentence is very normal and natural.