Курица ест зерно во дворе.

Because курица is the subject of the sentence, so it is in the nominative case.

• Dictionary form: курица
• Meaning here: a chicken / hen
• Gender: feminine
• Number: singular

So Курица ест... literally means The chicken eats...

Есть is the infinitive, meaning to eat.

In the sentence, we need a conjugated verb: eats.
So Russian uses ест, which is the 3rd person singular present tense form:

• я ем — I eat
• ты ешь — you eat
• он / она ест — he / she eats

Since курица is singular, ест is the correct form.

They look the same in the infinitive/dictionary form, but they are different words historically and function differently.

• есть = to eat (infinitive verb)
• есть = there is / there are or sometimes is in an emphatic/existential sense

In this sentence, ест clearly comes from есть = to eat, because it means eats.

Зерно is the direct object of ест, so you might expect the accusative case.
However, зерно is a neuter inanimate noun, and for many neuter inanimate nouns, the accusative singular looks exactly the same as the nominative singular.

So:

• nominative: зерно
• accusative: зерно

That is why the form does not change.

Зерно literally means grain or a grain/kernel.

In this kind of sentence, Russian often uses the singular the way English uses an uncountable noun:

• ест зерно = eats grain

If you said зёрна, that would sound more like grains / kernels as separate individual pieces.

So зерно is very natural here.

Russian sometimes uses во instead of в for easier pronunciation.

Here, the next word begins with дв-, and в дворе is awkward to say, so Russian prefers:

• во дворе

This is a common pronunciation-based variation.
The meaning is still the same as in the yard / in the courtyard.

Because after в / во when talking about location, Russian uses the prepositional case.

• dictionary form: двор
• prepositional singular: дворе

So:

• во дворе = in the yard / in the courtyard

The ending changes because the noun is inside a prepositional phrase showing location.

Because Russian distinguishes location and motion toward a place with case.

• во дворе = in the yard → location, so prepositional case
• во двор = into the yard → movement toward, so accusative case

In Курица ест зерно во дворе, the chicken is already there, eating there. So it is location, not motion.

Russian does not have articles like English a/an/the.

So курица can mean:

• a chicken
• the chicken

Which one is meant depends on context.
The same is true for зерно:

• grain
• the grain
• sometimes some grain

Russian leaves that to context instead of using articles.

The sentence uses a very normal, neutral word order:

• Курица — subject
• ест — verb
• зерно — object
• во дворе — location

So it feels like:

• The chicken eats grain in the yard.

Russian word order is more flexible than English because cases show grammatical roles. For example, you could also say:

• Во дворе курица ест зерно.

That would emphasize where it happens: In the yard, the chicken is eating grain.

So the original order is natural and straightforward, but not the only possible one.

It can mean either in different contexts:

• курица = a chicken / hen (the bird)
• курица = chicken (meat/food)

But in this sentence, because it is eating grain in the yard, it clearly means the animal, not the meat.

The standard stress is:

• ку́рица
• ест
• зерно́
• во дворе́

So the whole sentence is pronounced roughly:

• КУ-ри-ца ест зер-НО во два-РЕ

Stress matters in Russian, so it is worth learning words together with their stress.

Yes. Because Russian has no articles, and because курица can refer specifically to a hen/chicken, several English translations may fit depending on context:

• The chicken eats grain in the yard.
• A chicken eats grain in the yard.
• The hen is eating grain in the yard.
• A hen is eating grain in the yard.

If this is just an isolated example sentence, the exact English article choice depends on the translator, not on a separate Russian word.