Vejen er bred.

Because vejen is the definite form of the noun.

• en vej = a road
• vejen = the road

So the ending -en works like English the for this noun.
The basic dictionary form is vej.

In Danish, the definite article is often attached to the end of the noun instead of being a separate word.

So:

• en vej = a road
• vejen = the road

A separate article such as den is used in some other structures, especially when an adjective comes before the noun:

• den brede vej = the wide road

But in Vejen er bred, the noun stands alone, so the attached definite form vejen is the normal choice.

The noun vej is a common gender noun in Danish. That is why its indefinite article is en:

• en vej

Its main forms are:

• en vej = a road
• vejen = the road
• veje = roads
• vejene = the roads

So in the sentence, vejen is singular definite common gender.

Because bred agrees with the noun in gender and number, and here the subject is singular common gender.

Forms of the adjective:

• bred = common gender singular
• bredt = neuter singular
• brede = plural

So:

• Vejen er bred = The road is wide
• Huset er bredt = The house is wide
• Vejene er brede = The roads are wide

That is the difference between a predicative adjective and an attributive adjective.

In Vejen er bred, the adjective comes after er and describes the subject. That is a predicative adjective, so you use:

• bred

In den brede vej, the adjective comes before the noun. That is an attributive adjective, and in that structure Danish uses:

• den brede vej

So the two patterns are:

• Vejen er bred
• den brede vej

Both are correct; they just belong to different sentence structures.

Er is the present tense of at være, which means to be.

So:

• jeg er = I am
• du er = you are
• han er = he is
• vejen er = the road is

Unlike English, Danish does not change this form the way English changes am / is / are. The form er is used for all persons in the present tense.

A rough English approximation is VY-en.

Helpful notes:

• vej sounds roughly like vy or vigh
• the j sounds like English y
• the ending -en is usually weak and unstressed

The stress is on the first syllable: VEJ-en.

The exact Danish pronunciation is hard to capture in English spelling, but VY-en is a useful starting point.

A rough approximation is breth or brehd, but with a very soft final d.

Important point: Danish d at the end of a word is often not a hard English d. In bred, it is pronounced softly, somewhat like the th sound in this, though not exactly the same.

So do not pronounce it like a strong English bred-d.

You can form:

• Er vejen bred? = Is the road wide?
• Vejen er ikke bred. = The road is not wide.

So:

• for a yes/no question, Danish usually puts the verb first
• for negation, use ikke

Yes, vej can sometimes mean way in certain contexts, not only a physical road.

For example, Danish uses vej in some expressions about direction, route, or method. But in Vejen er bred, the meaning is clearly the physical sense: road.

So in this sentence, you should understand vej as road, not the more abstract English word way.