Моя мать работает в банке.

Because мать is a feminine noun, and the possessive word my has to agree with it.

• мой = masculine my
• моя = feminine my
• моё = neuter my
• мои = plural my

So:

• мой брат = my brother
• моя мать = my mother

Russian adjectives and possessives change form to match the noun’s gender, number, and case.

Both can mean mother / mom, but they feel different in style.

• мать = mother; more neutral, formal, or literary
• мама = mom / mum; warmer, more everyday, more common in speech

So Моя мать работает в банке sounds a bit more formal or matter-of-fact than:

• Моя мама работает в банке.

A learner will hear мама much more often in everyday conversation.

Работает is the 3rd person singular form of работать (to work), because the subject is моя мать = my mother / she.

Conjugation of работать in the present tense:

• я работаю = I work
• ты работаешь = you work
• он/она работает = he/she works
• мы работаем = we work
• вы работаете = you work
• они работают = they work

Since моя мать = she, Russian uses работает.

It can mean both, depending on context.

In this sentence, the most natural meaning is:

• My mother works in/at a bank.

That is, it describes her job or usual activity.

But Russian present tense often covers both:

• She works
• She is working

If the context were about what she is doing right now, работает could also mean is working.

Because after в when it means in / at a place, Russian usually uses the prepositional case.

• dictionary form: банк
• after в for location: в банке

So:

• в доме = in the house
• в школе = at school / in the school
• в банке = in the bank / at the bank

This is one of the most important Russian case patterns to learn:

• в + prepositional for location

Russian в often literally means in, but in English the most natural translation may be at.

So:

• работает в банке = literally works in a bank
• but very natural English: works at a bank

The Russian sentence does not force you to choose one exact English preposition in every context. English simply uses different prepositions more idiomatically.

There is no word for a or the here because Russian does not have articles.

So в банке could mean:

• in a bank
• in the bank
• at a bank
• at the bank

The exact meaning depends on context.

In this sentence, English usually says:

• My mother works at a bank or
• My mother works in a bank

If the speaker already has a specific bank in mind, English might use the, but Russian usually leaves that to context.

Yes. Russian word order is more flexible than English because case endings show grammatical roles.

The neutral order here is:

• Моя мать работает в банке.

But you could also say:

• В банке работает моя мать.
• Работает моя мать в банке.

These alternatives may change the emphasis:

• Моя мать работает в банке. = neutral statement
• В банке работает моя мать. = emphasizes at a bank
• Моя мать в банке работает. = possible in speech, often contrastive or stylistically marked

So the original order is the best basic version for learners.

The stress is:

• моЯ
• мать
• рабОтает
• в бАнке

So the sentence is pronounced approximately:

• ma-YA mat' ra-BO-ta-yet v BAN-kye

A few notes:

• я in моя sounds like ya
• ть in мать is a soft consonant
• е in банке after к sounds like ye
• unstressed vowels are reduced in real speech, so pronunciation is not always exactly like the spelling suggests

Yes, a little. Мать is a very common word, but its forms are somewhat irregular compared with many other nouns.

In this sentence, you only need the nominative form:

• мать

But in other cases you may see forms like:

• матери
• матью is not standard; the standard instrumental is матерью

So it is a good word to memorize carefully as you continue learning. In this sentence, though, it is simply the subject in the nominative case.