Wenn das Brett nicht waagerecht hängt, müssen wir noch einmal messen.

Because wenn introduces a subordinate clause, and in German subordinate clauses the finite verb normally goes to the end.

So the pattern is:

wenn + subject + other elements + finite verb

Here:

• wenn = if
• das Brett = the board
• nicht waagerecht = not level / not horizontal
• hängt = is hanging

That is why German says:

Wenn das Brett nicht waagerecht hängt ...

and not Wenn das Brett hängt nicht waagerecht.

German main clauses follow the verb-second rule: the finite verb must come in the second position.

In this sentence, the whole wenn-clause comes first:

Wenn das Brett nicht waagerecht hängt, ...

That entire clause counts as position 1. So the finite verb of the main clause must come next, in position 2:

..., müssen wir noch einmal messen.

If you started with the main clause instead, you would say:

Wir müssen noch einmal messen, wenn das Brett nicht waagerecht hängt.

Both are correct.

Das Brett is nominative singular because it is the subject of the clause.

It is the thing that is doing the action/state of hängen:

• das Brett hängt = the board is hanging

Brett is a neuter noun, so:

• nominative singular: das Brett
• accusative singular: das Brett

In this sentence, the form happens to look the same in nominative and accusative, but its job is nominative because it is the subject.

Because waagerecht is being used predicatively, not directly before a noun.

Compare:

• das waagerechte Brett = the level/horizontal board
  
  • here the adjective comes before the noun, so it gets an ending
• das Brett ist waagerecht
• das Brett hängt waagerecht
  
  • here the adjective describes the subject after the verb, so it has no ending

This is similar to English:

• the level board
• the board is level

Because the sentence is talking about the board’s state while hanging.

hängen means to hang / to be hanging. So:

• Das Brett hängt waagerecht. = The board is hanging level.

Using sein would also be grammatically possible in some contexts:

• Das Brett ist nicht waagerecht.

But that sounds more general: the board is not level.
With hängt, the sentence focuses on the board as it is hanging.

That is especially natural if you are checking whether something mounted on a wall is straight.

Waagerecht means horizontal or level.

In this context, a very natural English meaning is level:

• wenn das Brett nicht waagerecht hängt
  = if the board isn’t hanging level

A close opposite is senkrecht = vertical.

German also has horizontal, but waagerecht is very common in everyday language.

Here, wenn means if.

The sentence gives a condition:

• If the board isn’t hanging level, we need to measure again.

German wenn can mean:

• if
• when
• whenever

You decide from context.

In this sentence, it is clearly conditional, so if is the best translation.

Noch einmal literally means once more or one more time. In many contexts, it is translated simply as again.

So:

Wir müssen noch einmal messen.
= We need to measure again / one more time.

Compared with wieder:

• noch einmal often emphasizes the idea of doing the action one more time
• wieder is the more general word for again

In this sentence, both would sound natural:

• Wir müssen noch einmal messen.
• Wir müssen wieder messen.

But noch einmal can feel slightly more like let’s repeat the measuring process once more.

Because the sentence uses the modal verb müssen.

With a modal verb in a main clause:

• the finite modal verb goes in the normal verb position
• the main verb stays in the infinitive at the end

So:

• wir müssen messen = we must measure

In your sentence:

• müssen = finite modal verb
• messen = infinitive at the end

That gives:

..., müssen wir noch einmal messen.

Because German normally puts a comma before or after a subordinate clause, including one introduced by wenn.

So this is standard punctuation:

Wenn das Brett nicht waagerecht hängt, müssen wir noch einmal messen.

The comma marks the boundary between:

• the subordinate clause: Wenn das Brett nicht waagerecht hängt
• the main clause: müssen wir noch einmal messen

This comma is required in standard German.