Подразделение ГИБДД проверяет место регистрации.

ГИБДД is an abbreviation for Государственная инспекция безопасности дорожного движения.

In everyday Russian, it refers to the traffic police / road safety authority. In this sentence, подразделение ГИБДД means a department/unit of the traffic police.

A useful thing to remember: Russians very often use abbreviations like this, especially for government agencies.

Because подразделение is a singular noun: a subdivision / a department / a unit.

So the verb agrees with it:

• подразделение ... проверяет = the department checks
• not проверяют, which would be plural

Also, подразделение is grammatically neuter, which is why in the present tense the verb has the regular 3rd person singular form проверяет.

It is in the nominative case, because it is the subject of the sentence — the thing doing the action.

• подразделение = nominative singular
• ГИБДД stays in abbreviation form and functions like of the traffic police

So the whole subject is подразделение ГИБДД = the traffic police department/unit.

Проверяет comes from the verb проверять, which is imperfective.

Here that makes sense because the sentence describes a general action or procedure:

• проверяет = checks / is checking

If you used the perfective verb проверит, that would usually mean will check or checks once and completes it in the future.

So in a neutral factual sentence like this, проверяет is the natural choice.

Место is in the accusative case, because it is the direct object of проверяет.

However, место is a neuter inanimate noun, and for many neuter inanimate nouns the accusative form is identical to the nominative:

• nominative: место
• accusative: место

So even though it looks unchanged, it is functioning as the object.

Because регистрации is in the genitive singular.

The phrase место регистрации literally means:

• место = place
• регистрации = of registration

So it is a standard noun + noun construction in Russian, where the second noun often goes into the genitive:

• адрес дома = the address of the house
• номер паспорта = passport number
• место регистрации = place of registration

Yes, absolutely.

ГИБДД проверяет место регистрации would mean something like the traffic police check the place of registration.

Adding подразделение makes it a bit more specific or bureaucratic:

• ГИБДД = the traffic police as an institution
• подразделение ГИБДД = a specific department/unit of that institution

Russian official language often uses nouns like подразделение, орган, отдел, служба, and so on.

Yes. Russian word order is fairly flexible, because case endings show the grammatical roles.

The neutral order here is:

• Подразделение ГИБДД проверяет место регистрации.

But other orders are possible, depending on emphasis:

• Место регистрации проверяет подразделение ГИБДД.
  This puts more focus on место регистрации.
• Проверяет место регистрации подразделение ГИБДД.
  This is less neutral and more stylistic or context-dependent.

For a learner, the original order is the best default: subject + verb + object.

Russian has no articles.

So подразделение can mean:

• a department
• the department

and место регистрации can mean:

• a place of registration
• the place of registration

The exact meaning depends on context. That is normal in Russian.

Проверяет is pronounced roughly pra-vye-RYA-yet.

It is the 3rd person singular present-tense form of проверять:

• я проверяю = I check
• ты проверяешь = you check
• он / она / оно проверяет = he / she / it checks
• они проверяют = they check

The ending -ет is part of the normal conjugation pattern here.

Also notice the stress: проверЯет.

Not exactly.

Место регистрации literally means place of registration. Depending on context, it may refer to the officially registered residence or registered location.

It overlaps with the idea of an official registered address, but it is not always exactly the same as the everyday word адрес.

For example:

• адрес = address
• место регистрации = place of registration / registered residence

In bureaucratic or legal contexts, место регистрации is often more precise than just адрес.