Покриття мережі хороше.

In Ukrainian, the present-tense verb to be is usually omitted in simple statements.

So:

Покриття мережі хороше.

literally looks like:

Network coverage good.

But it naturally means The network coverage is good or Network coverage is good.

This is completely normal Ukrainian. English needs is here; Ukrainian usually does not.

Мережі is the genitive singular form of мережа.

Here, покриття мережі means coverage of the network. Ukrainian often uses this pattern:

noun + genitive noun

to show a relationship like of the network, of the city, of the company, etc.

So:

• мережа = network
• мережі = of the network

Because it agrees with покриття, which is a neuter singular noun.

In Ukrainian, adjectives must agree with the noun they describe in gender, number, and case.

Here are the basic singular forms of good:

• masculine: хороший
• feminine: хороша
• neuter: хороше

Since покриття is neuter, the sentence uses хороше.

Покриття is a neuter noun. One clue is its ending: many Ukrainian nouns ending in -ття are neuter.

Also, the adjective agrees with it as хороше, which confirms that the noun is neuter.

So in this sentence:

• покриття = neuter singular
• хороше = neuter singular adjective matching it

A simple breakdown is:

• Покриття мережі = the subject phrase
• хороше = the predicate adjective

So the structure is:

[subject] + [description]

More literally:

The network's coverage [is] good.

It is an adjective.

Even though the sentence has no written is, хороше is still describing the noun покриття, not modifying a verb.

So it is a predicate adjective: it tells us what the subject is like.

That is why it agrees with покриття in neuter singular form.

Yes, Ukrainian word order is more flexible than English word order.

The neutral, straightforward version is:

Покриття мережі хороше.

You might also see:

Хороше покриття мережі.

But that version is more like Good network coverage as a noun phrase, or it can shift the emphasis.

For a plain statement meaning The network coverage is good, your original sentence is a very natural order.

Ukrainian does not have articles like a and the.

So Покриття мережі хороше can be translated depending on context as:

• The network coverage is good
• Network coverage is good

English must choose an article or leave it out; Ukrainian does not.

A helpful stress-marked version is:

покрИття мережІ хорОше

A rough English-friendly approximation is:

po-KRYT-tya me-re-ZHI kho-RO-she

A couple of sound notes:

• х sounds like the ch in Scottish loch or German Bach
• ж sounds like the s in measure

Yes. That is the literal structure.

• покриття = coverage
• мережі = of the network

So the sentence is literally:

Coverage of the network [is] good.

In natural English, that often becomes The network coverage is good or The coverage is good depending on context.