Mater infantem in lecto ponit, et infans statim dormit.

Because the noun changes form depending on its job in the sentence.

• mater = mother as the subject of ponit
• infantem = the baby/child as the direct object of ponit
• infans = the baby/child again, but now as the subject of dormit

So:

• Mater infantem ponit = The mother puts the baby
• infans dormit = the baby sleeps

Latin shows these roles with case endings, not mainly by word order.

infantem is accusative singular.

It is used because the baby is the direct object of ponit: the mother is putting the baby somewhere.

A very common beginner pattern is:

• subject in the nominative
• direct object in the accusative

So here:

• mater = nominative subject
• infantem = accusative object

Because in can take two different cases depending on the meaning:

• in + ablative = in/on a place, showing location
• in + accusative = into/onto a place, showing motion toward

Here we have in lecto, with lecto in the ablative. That means the baby is being placed in/on the bed, with emphasis on the place where the baby ends up.

For a beginner, it is helpful to remember:

• in lecto = in/on the bed
• in lectum = into/onto the bed

In real Latin, pono in + ablative is very normal for place something in/on a place.

lecto is ablative singular of lectus, meaning bed.

It is ablative because it follows in in the sense of location:

• in lecto = in/on the bed

So the phrase tells you where the baby is placed.

ponit is from pono, ponere, and here it means puts, places, or lays.

So Mater infantem in lecto ponit can be understood as:

• The mother puts the baby on the bed
• The mother places the baby in the bed
• The mother lays the baby on the bed

All of those are reasonable translations depending on context.

Grammatically, ponit is:

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

So it means she puts or the mother puts.

Because Latin has no articles.

English says:

• the mother
• a baby
• the bed

Latin usually just says:

• mater
• infans / infantem
• lectus / lecto

Whether you translate as a or the depends on the context. In this sentence, English naturally uses the mother, the baby, and the bed, but Latin itself does not explicitly mark that.

It matters somewhat for style and emphasis, but less than in English.

Because Latin uses case endings, you can tell who is doing what even if the order changes:

• Mater infantem in lecto ponit
• Infantem mater in lecto ponit
• In lecto mater infantem ponit

All of these can still mean roughly The mother puts the baby on the bed.

The given order is straightforward and easy to read. Latin often puts the verb later in the clause, as here with ponit and dormit.

statim is an adverb meaning immediately, at once, or right away.

So:

• infans statim dormit = the baby immediately falls asleep / sleeps at once

In Latin, adverbs often have fairly flexible position. statim is placed before dormit here, which is very natural.

Because Latin normally uses a simple finite verb for sleeps:

• dormit = he/she/it sleeps

You do not need an extra verb like is sleeping unless you are trying to express something different in English. Latin often uses the simple present where English might use either:

• sleeps
• is sleeping

depending on context.

So infans statim dormit is perfectly normal Latin.

dormit is:

• present tense
• 3rd person singular
• from dormio, dormire = to sleep

So it means:

• he sleeps
• she sleeps
• the baby sleeps

Since infans is singular, the verb is singular too.

It can mean both, depending on context.

infans literally originally meant something like not speaking, and it can refer to:

• an infant
• a baby
• a young child

So in this sentence, English might translate it as baby or child, depending on the situation shown.

Because Latin verb endings already tell you the person and number.

• ponit = he/she/it puts
• dormit = he/she/it sleeps

And the nouns make the subject clear:

• mater ... ponit = the mother puts
• infans ... dormit = the baby sleeps

So Latin often does not need subject pronouns unless it wants extra emphasis or contrast.

That is just how this noun declines.

infans is a 3rd-declension noun. Its nominative singular is infans, while its accusative singular is infantem.

So you get:

• infans = subject form
• infantem = object form

This is very common in the 3rd declension: the nominative can look quite different from the other cases, while forms like the accusative often use more regular endings.