Мне очень нравится фильм, который мы смотрели вчера.

Because нравиться works differently from English to like.

In Russian, мне нравится фильм literally works more like:

• The film is pleasing to me
• To me, the film is appealing

So:

• мне = to me (dative case)
• фильм = the thing that is liked

That is why Russian uses мне, not я.

Compare:

• Я люблю фильм = I love the film
• Мне нравится фильм = I like the film

These are two different structures.

Because the verb agrees with фильм, not with мне.

In this sentence, the subject is фильм, so the verb is in 3rd person singular:

• фильм нравится = the film is pleasing / the film appeals

So:

• мне нравится фильм = I like the film

Not:

• я нравлюсь = I am liked
• я нравлю = not how this verb is normally used here

A useful rule:

• If one thing is liked: нравится
• If multiple things are liked: нравятся

Examples:

• Мне нравится фильм. = I like the film.
• Мне нравятся фильмы. = I like films.

Because with нравиться, the thing being liked is the grammatical subject.

In English, I like the film makes I the subject and film the object.

In Russian, Мне нравится фильм makes:

• мне = indirect experiencer, in the dative
• фильм = subject, in the nominative

So фильм stays in the nominative.

This is one of the most important differences between English like and Russian нравиться.

Очень means very.

So:

• Мне нравится фильм = I like the film.
• Мне очень нравится фильм = I really like the film / I like the film very much.

Its usual position is before the verb or before the word it modifies. In this sentence, очень нравится is the most natural placement.

You may also hear slightly different word orders, but Мне очень нравится фильм is standard and natural.

Because который мы смотрели вчера is a relative clause: it describes фильм.

Russian normally separates relative clauses with a comma.

So:

• фильм = the film
• который мы смотрели вчера = that / which we watched yesterday

Together:

• фильм, который мы смотрели вчера = the film that we watched yesterday

This comma is required in standard Russian punctuation.

Который is the relative pronoun meaning which, that, or the one that, depending on context.

It refers back to фильм.

Since фильм is:

• masculine
• singular

the relative pronoun appears here as который.

It must also match the role it plays inside the relative clause. In который мы смотрели вчера, it is the direct object of смотрели, so который is in the accusative form. For an animate masculine noun, nominative and accusative would differ, but for an inanimate masculine noun like фильм, the form looks the same here: который.

Because фильм is masculine singular inanimate, and for that type of noun/pronoun, the accusative often looks the same as the nominative.

So although который is functioning as the object of смотрели, its form is still который.

Compare with an animate masculine example:

• человек, которого мы видели = the person whom we saw

Here you can clearly see the accusative form которого.

But with an inanimate masculine noun:

• фильм, который мы смотрели = the film that we watched

So the form may look unchanged even though the grammatical case is different.

Because the subject of that clause is мы.

In the relative clause:

• мы смотрели вчера = we watched yesterday

Since мы means we, the verb must be plural:

• я смотрел / смотрела
• мы смотрели

So смотрели agrees with мы, not with фильм.

Because вчера means yesterday, so the action happened in the past.

That is why Russian uses the past tense:

• мы смотрели вчера = we watched yesterday

Russian past tense often makes time very clear when used with words like:

• вчера = yesterday
• сегодня = today
• завтра = tomorrow

Here, вчера strongly requires a past-time interpretation.

This is a question of aspect.

• смотреть / смотрели = imperfective
• посмотреть / посмотрели = perfective

Both can sometimes be translated as watched, but they emphasize different things.

Here, смотрели sounds natural because it refers to the process or fact of watching the film.

• фильм, который мы смотрели вчера = the film that we were watching / watched yesterday

You could also hear который мы посмотрели вчера in some contexts, especially if the speaker wants to emphasize completion: the film that we watched all the way through yesterday.

So:

• смотрели = neutral, process/fact
• посмотрели = completed event

In this sentence, смотрели is very natural.

Yes, Russian word order is flexible, but not all versions sound equally natural in every context.

The neutral version is:

• Мне очень нравится фильм, который мы смотрели вчера.

Other orders are possible for emphasis, for example:

• Фильм, который мы смотрели вчера, мне очень нравится.

This version puts more focus on the film we watched yesterday.

Russian word order often changes to reflect emphasis, topic, or style, while the case endings still show the grammatical roles.

Yes, as a learning tool, that can actually help.

A rough literal breakdown is:

• Мне = to me
• очень = very
• нравится = is pleasing / appeals
• фильм = the film
• который мы смотрели вчера = that we watched yesterday

So a literal memory version like To me, the film we watched yesterday is very pleasing can help you remember the grammar.

But in natural English, you would simply say:

• I really like the film we watched yesterday.

It can mean both, depending on natural English style.

In this sentence:

• фильм, который мы смотрели вчера

could be translated as:

• the film that we watched yesterday
• the film which we watched yesterday

In modern English, that is often more natural here. Russian uses который where English may use either that or which.

So you should not expect a one-to-one match between который and only which.

Then the noun and the verb would both change:

• Мне очень нравятся фильмы, которые мы смотрели вчера.

Changes:

• нравится → нравятся because the subject is now plural
• фильм → фильмы
• который → которые to match the plural noun

So the pattern is:

• singular: Мне нравится фильм, который...
• plural: Мне нравятся фильмы, которые...