Mia kuzo atendas nin ĉe la stacidomo.

Because mia is the possessive form of mi.

• mi = I
• mia = my

In Esperanto, possessive words usually end in -a, because they behave like adjectives:

• mia kuzo = my cousin
• via domo = your house
• lia libro = his book

So mia kuzo literally means my cousin.

By itself, kuzo is often understood as cousin without emphasizing gender, but traditionally it is the masculine form.

• kuzo = male cousin / cousin
• kuzino = female cousin

The suffix -in- marks female gender in Esperanto. So if you want to make it explicit that the cousin is female, you would say mia kuzino.

The ending -as marks the present tense in Esperanto.

So:

• atendi = to wait
• atendas = waits / is waiting / wait

Esperanto verb endings are very regular:

• -as = present
• -is = past
• -os = future
• -us = conditional
• -u = command or wish
• -i = infinitive

So mia kuzo atendas means my cousin is waiting or my cousin waits.

Because nin is the accusative form, used for the direct object.

• ni = we
• nin = us

In this sentence, my cousin is doing the action, and us is receiving the action of waiting for:

• Mia kuzo = subject
• atendas = verb
• nin = direct object

Esperanto usually adds -n to mark the direct object:

• mi → min
• vi → vin
• li → lin
• ŝi → ŝin
• ni → nin
• ili → ilin

So atendas nin = is waiting for us.

Because in Esperanto, atendi directly takes an object. English says wait for someone, but Esperanto simply says atendi iun.

So:

• Mi atendas vin. = I am waiting for you.
• Ŝi atendas la buson. = She is waiting for the bus.

This is a common thing learners need to remember: Esperanto does not always match English prepositions. With atendi, you normally use the direct object, not a preposition.

ĉe means something like at, by, or with, depending on context. In this sentence, it means at.

• ĉe la stacidomo = at the train station

ĉe is often used for location in relation to a place or person:

• Mi estas ĉe la domo. = I am at the house.
• Ŝi loĝas ĉe sia onklino. = She lives with her aunt.
• Ni renkontiĝos ĉe la stacidomo. = We will meet at the station.

So here it tells you where your cousin is waiting.

La is the definite article, meaning the.

• stacidomo = a station / station
• la stacidomo = the station

Esperanto has only one article, la, and it never changes for gender, number, or case.

In this sentence, la stacidomo probably refers to a specific station already known from context, so the station is natural.

Yes. Stacidomo is a compound word.

It can be broken down like this:

• staci- = station-related stem
• domo = building, house

So stacidomo is literally something like station-building.

In practice, it means station, and very often specifically railway station / train station.

Esperanto forms many words this way, by combining meaningful parts into one clear compound.

Usually yes, or at least that is the most common interpretation.

If you want to be very explicit, you could say:

• fervoja stacidomo = railway station

But in ordinary usage, stacidomo commonly means train station. Context usually makes it clear.

The sentence follows the most common Esperanto word order:

subject + verb + object + other information

So here:

• Mia kuzo = subject
• atendas = verb
• nin = object
• ĉe la stacidomo = place phrase

This is very similar to English: My cousin is waiting for us at the station.

Esperanto word order is fairly flexible, but this order is the most neutral and easiest for learners.

Yes, to some extent. Esperanto allows flexible word order, especially because the -n ending helps show the object.

For example, these are still understandable:

• Ĉe la stacidomo mia kuzo atendas nin.
• Nin atendas mia kuzo ĉe la stacidomo.

Because nin has -n, you still know it is the object.

However, Mia kuzo atendas nin ĉe la stacidomo is the most neutral and natural order for beginners to learn first.

Ĉ is pronounced like ch in church.

So ĉe sounds roughly like cheh.

A quick pronunciation guide for the whole sentence:

• Mia = MEE-ah
• kuzo = KOO-zoh
• atendas = ah-TEN-dahs
• nin = neen
• ĉe = cheh
• la = lah
• stacidomo = stah-tsee-DOH-moh

Esperanto pronunciation is very regular, so once you know the letters, words are usually easy to sound out.

Actually, if needed, it would change. Adjectives and similar words in Esperanto agree with the noun they describe in number and case.

Here, kuzo is singular and not accusative, so:

• mia kuzo = correct

If the noun were plural or accusative, mia would change too:

• miaj kuzoj = my cousins
• mian kuzon = my cousin (as direct object)
• miajn kuzojn = my cousins (as direct object)

So in this sentence, mia stays simple because kuzo is singular and is the subject.

Sometimes atendi can also mean expect, depending on context. That is similar to English to expect or to await.

Examples:

• Mi atendas vin. = I am waiting for you.
• Mi atendas bonajn novaĵojn. = I expect good news.

In your sentence, because the object is nin and there is a location phrase ĉe la stacidomo, the natural meaning is clearly is waiting for us.