Servus laborem ingratum vitat.

Because servus is in the nominative singular, the case normally used for the subject.

• servus = nominative singular
• so it means the slave or a slave as the doer of the action

In this sentence, servus is the one doing the avoiding.

Because laborem is in the accusative singular, the case used for a direct object.

The direct object is the thing being acted on. Here, it is the thing being avoided.

• nominative: labor = work, labor
• accusative: laborem = work, labor as the object of the verb

So laborem tells you what the slave avoids.

Because ingratum is an adjective modifying laborem, and Latin adjectives must agree with the nouns they describe in:

• gender
• number
• case

Here:

• laborem is masculine
• singular
• accusative

So the adjective must match it:

• ingratum = masculine, singular, accusative

Even though laborem ends in -em and ingratum ends in -um, they still agree because they belong to different declension patterns.

vitat is:

• 3rd person singular
• present tense
• active voice
• indicative mood

It comes from vitare, meaning to avoid.

So vitat means he avoids, she avoids, or it avoids.
Because the subject here is servus, we understand it as the slave avoids.

Latin often does not need a separate subject pronoun because the verb ending already tells you the person and number.

In vitat, the ending -t means he/she/it (3rd person singular).

So even without servus, vitat could already mean he avoids, she avoids, or it avoids.
The noun servus is added to make the subject explicit.

Classical Latin has no articles.

So servus can mean:

• the slave
• a slave

And laborem ingratum can mean:

• the unpleasant work
• an unpleasant task
• unpleasant work

You decide from the context which English article sounds best.

We know because of the case endings, not because of word order.

• servus = nominative = subject
• laborem = accusative = direct object

So the grammar tells us:

• servus is doing the action
• laborem ingratum is receiving the action

That is one of the most important differences from English, which relies much more heavily on word order.

It is important stylistically, but less important grammatically than in English.

Latin word order is relatively flexible because the endings show each word’s role.
So all of these could express basically the same core meaning:

• Servus laborem ingratum vitat.
• Servus ingratum laborem vitat.
• Laborem ingratum servus vitat.

That said, the original order is very natural:

• subject first: servus
• object next: laborem ingratum
• verb last: vitat

Putting the verb at the end is especially common in Latin.

Literally, ingratus, -a, -um often means unpleasant, disagreeable, unwelcome, or sometimes ungrateful, depending on context.

With a thing like labor, the sense is usually something like:

• unpleasant
• thankless
• disagreeable

So in this sentence it describes the work as something undesirable or not rewarding.

Because Latin often puts adjectives after the nouns they modify, although it can also place them before.

So:

• laborem ingratum
• ingratum laborem

both mean the same basic thing.

The choice can depend on style, emphasis, rhythm, or author preference. A learner should get used to adjectives appearing either before or after the noun.

You would normally look them up like this:

• servus, servi = slave
• labor, laboris = work, labor
• ingratus, ingrata, ingratum = unpleasant, thankless, ungrateful
• vito, vitare, vitavi, vitatum = avoid

Latin dictionaries usually give nouns in the nominative singular + genitive singular, adjectives in their masculine/feminine/neuter forms, and verbs in their principal parts.

In Classical Latin, servus usually means slave more than servant.

A native English speaker may be tempted to soften it to servant, but in Roman society servus normally refers to someone who is enslaved.

So unless context suggests otherwise, slave is the more accurate basic translation.