Na tom travnjaku djeca ne smiju trčati dok je zemlja mokra.

Because na means on here, and when it refers to a static location, it usually takes the locative case.

• base form: travnjak = lawn
• locative singular: travnjaku = on the lawn

So na tom travnjaku means on that lawn.

A useful contrast:

• na travnjaku = on the lawn, located there
• na travnjak = onto the lawn, movement toward it

Here there is no movement onto the lawn, just location, so the locative is used.

Because tom is the form of taj that matches the locative singular.

The demonstrative taj changes its form depending on case, just like adjectives do.

For masculine singular, some forms are:

• nominative: taj travnjak = that lawn
• locative: na tom travnjaku = on that lawn

So tom is not a different word; it is just the correct case form of taj here.

It means children, so it is plural in meaning, and it takes plural agreement:

• djeca ne smiju = the children must not / are not allowed to

Its singular is dijete = child.

This plural is irregular:

• singular: dijete
• plural: djeca

So even though djeca may look unusual to an English speaker, it behaves as a plural noun in sentences like this one.

Ne smiju comes from smjeti, which means to be allowed to / may.

So:

• smiju trčati = they may run / they are allowed to run
• ne smiju trčati = they may not run / they are not allowed to run

In natural English, this is often best translated as must not run or are not allowed to run.

This is different from ne mogu trčati, which would mean they cannot run in the sense of inability, not prohibition.

Because smjeti is a modal verb, and modal verbs are followed by the infinitive of the main verb.

So:

• smjeti + infinitive
• ne smiju trčati = they are not allowed to run

This works like English may run, must run, can run, except Croatian uses the infinitive form directly.

Here dok means while or as long as.

So:

• dok je zemlja mokra = while the ground is wet / as long as the ground is wet

That fits the meaning of a temporary condition: the children must not run during the time when the ground is wet.

In other contexts, dok can sometimes be translated differently, but here while / as long as is the natural meaning.

Because je is a clitic in Croatian. Clitics are short unstressed words that usually go in the second position of their clause.

So after dok, it is natural to say:

• dok je zemlja mokra

and not:

• dok zemlja je mokra

The second version sounds unnatural in standard Croatian.

This second-position behavior is very common with Croatian clitics such as:

• je, su
• se
• ga, je, im, etc.

Because mokra is an adjective agreeing with zemlja.

• zemlja is feminine singular
• so the adjective must also be feminine singular: mokra

Compare:

• mokar travnjak = a wet lawn
• mokra zemlja = wet ground
• mokro dijete = a wet child

So zemlja je mokra literally means the ground is wet, with the adjective matching the noun in gender and number.

Zemlja can mean several things depending on context:

• earth
• land
• country
• soil / ground

In this sentence, it means ground or soil, not the planet Earth and not country.

So the idea is that the lawn should not be run on while the ground/soil is wet.

Yes, Croatian word order is more flexible than English, but the sentence as given is a very natural, neutral way to say it.

For example, you might also hear:

• Djeca ne smiju trčati na tom travnjaku dok je zemlja mokra.

This still means the same thing. The original sentence simply puts na tom travnjaku first for emphasis or topic, something like On that lawn, children must not run while the ground is wet.

So the word order can shift, but the version you have is completely normal.