Ez a régiség az előző századból van.

In Hungarian, when a demonstrative like ez (this) or az (that) comes directly before a noun, it normally appears together with the definite article.

So:

• ez a régiség = this antique
• az a ház = that house

This is standard Hungarian structure. English does not do this, but Hungarian does.

So ez régiség would sound incomplete or ungrammatical in normal usage.

Hungarian has two forms of the definite article:

• a before a consonant sound
• az before a vowel sound

So:

• a régiség because régiség starts with r
• az előző because előző starts with e

This is similar to English a/an, but Hungarian uses the distinction only in pronunciation/form, not in indefiniteness.

Régiség means something old, especially an antique, an antique object, or sometimes an antiquity.

In this sentence, ez a régiség most naturally means:

• this antique
• this antique object

It is a noun, not an adjective. So it does not mean old by itself.
If you wanted old as an adjective, you would use régi.

Compare:

• régi tárgy = old object
• régiség = antique / antiquity

Előző means previous or preceding.

So az előző század literally means the previous century.

Depending on context, English might also translate this as the last century, but előző is more literally previous.

A nearby alternative is:

• a múlt század = the last century / the past century

In many contexts, az előző századból van and a múlt századból van are very close in meaning.
Still, előző focuses more on the one before this one, while múlt focuses more on past.

Because Hungarian uses case endings instead of separate prepositions in many situations.

The ending -ból / -ből means out of / from.

So:

• század = century
• századból = from the century

In this sentence, az előző századból means from the previous century.

This ending is often used not only for literal movement out of something, but also for origin or source. Here it expresses that the antique dates from that century.

This is because of vowel harmony, which is a major feature of Hungarian.

Hungarian suffixes often have a back-vowel form and a front-vowel form:

• -ból after back-vowel words
• -ből after front-vowel words

Század contains back vowels (á, a), so it takes -ból:

• század → századból

A front-vowel example:

• szék → székből = out of the chair

So the suffix changes to match the type of vowels in the word.

That is a very common and important question.

Hungarian often omits van in the 3rd person singular/plural present tense when the predicate is a noun or adjective:

• Ez egy régiség. = This is an antique.
• A ház nagy. = The house is big.

But in this sentence, the predicate is not just a noun or adjective. It includes a phrase of origin/source:

• az előző századból van = is from the previous century

In this kind of sentence, van is normally kept.

So:

• Ez a régiség az előző századból van. = correct

If you removed van, the sentence would sound incomplete.

Yes, Hungarian word order is flexible, but it is not random. It often reflects topic and focus.

In this sentence:

• Ez a régiség = the topic, what we are talking about
• az előző századból van = what we say about it

So the sentence feels like:

• As for this antique, it is from the previous century.

Other word orders are possible, but they may change the emphasis.

For example:

• Ez a régiség az előző századból van.
  Neutral, natural statement.

• Az előző századból van ez a régiség.
  More emphasis on from the previous century.

For learners, the original order is the best neutral pattern to copy.

Yes, század is the normal word for century.

• század = century
• évszázad = literally hundred-year period, also century

In many contexts they overlap, but század is the ordinary historical term, especially for things like:

• a 19. század = the 19th century
• múlt század = last century

So in this sentence, század is completely natural.

Not with the same meaning.

• Ez a régiség az előző századból van. = This antique is from the previous century.

If you say:

• Ez az előző századból van.

then ez means this, but there is no noun like régiség telling us what this is. That can work only if the object is already very clear from context, and it means more like:

• This one is from the previous century.

So the original sentence is fuller and clearer because it explicitly names the object as a régiség.

A few useful pronunciation points:

• ez a: the z links smoothly to the next word
• régiség: both é sounds are long
• előző: ő is a long front rounded vowel; both ő sounds are long
• századból: the á is long, and ból also has a long ó

Very roughly for an English speaker:

• Ez a régiség az előző századból van
• EHZ aw RAY-ghee-shayg awz EL-oh-zoh SAA-zawd-bohl vawn

That is only approximate, but it helps show where the long vowels are. In Hungarian, vowel length matters, so é / e, á / a, and ó / o should be distinguished clearly.