Это рюкзак, с которым я хожу в университет каждый день.

It means with which or, more naturally in English, that I go with.

So:

• рюкзак = backpack
• с которым = with which / with that
• я хожу в университет каждый день = I go to university every day

A very literal version would be:

This is the backpack with which I go to university every day.

In natural English, we usually say:

This is the backpack that I take to university every day.

Because the pronoun который changes form depending on its role in the clause.

Here it refers back to рюкзак, but it is used after the preposition с. The preposition с in this meaning (with) normally requires the instrumental case.

So:

• dictionary form: который
• after с: с которым

Also, it must agree with рюкзак, which is:

• masculine
• singular

That is why the form is которым:

• masculine
• singular
• instrumental

Because который is a relative pronoun, and in Russian it agrees with the noun it refers to in:

• gender
• number

Here it refers to рюкзак, which is masculine singular, so которым is also masculine singular.

But its case is determined by its function inside the relative clause, not by рюкзак in the main clause.

So in this sentence:

• gender/number come from рюкзак
• case comes from с in с которым

That is a very important pattern in Russian relative clauses.

Because с которым я хожу в университет каждый день is a relative clause describing рюкзак.

Russian normally separates relative clauses with a comma:

• Это рюкзак, с которым...

This works much like English:

• This is the backpack, which/that...

In English, punctuation depends on style and meaning, but in Russian the comma before this kind of descriptive clause is standard.

Because хожу expresses a habitual, repeated, regular action, while иду usually means a single action happening now in one direction.

Compare:

• Я хожу в университет каждый день. = I go to university every day.
• Я иду в университет. = I am going to university / I’m on my way to university.

Since the sentence includes каждый день (every day), the repeated-motion verb ходить is the correct choice, and the 1st person singular form is хожу.

Because the sentence describes motion to a place, not being in a place.

Russian often uses:

• в + accusative for motion into/to somewhere
• в + prepositional for location in/at somewhere

So:

• в университет = to the university / to university
• в университете = in/at the university

Here the speaker is going there, so в университет is correct.

Because Russian has no articles.

English distinguishes between:

• a backpack
• the backpack
• to the university
• to university

Russian does not use words like a or the. The exact meaning comes from context.

So Это рюкзак... can mean:

• This is a backpack...
• This is the backpack...

But in this sentence, the context strongly suggests:

This is the backpack that I take to university every day.

Это here means this is.

Russian often omits the verb to be in the present tense, so:

• Это рюкзак literally looks like This backpack
• but it means This is a backpack / This is the backpack

So the full sentence starts by identifying something:

Это рюкзак... = This is the backpack...

This is a very common Russian pattern.

The given sentence focuses on the backpack as something the speaker goes with.

• с которым я хожу в университет = that I go to university with
• который я ношу в университет = that I carry/wear to university

Both can be possible depending on nuance, but they are not exactly the same.

с которым я хожу sounds natural when the backpack is part of the speaker’s usual routine or accompanies them.

который я ношу emphasizes physically carrying or wearing it.

In English, we often translate both quite naturally as:

the backpack I take to university every day

Каждый день is in the accusative case.

This is a common Russian time expression meaning every day.

The adjective-noun pair is:

• каждый = every
• день = day

In this kind of adverbial time expression, Russian often uses the accusative:

• каждый день = every day
• каждую неделю = every week
• каждый год = every year

So here it functions like an adverb of frequency.

Yes. Russian word order is flexible, though different orders can change the emphasis.

The given sentence:

Это рюкзак, с которым я хожу в университет каждый день.

is perfectly natural and emphasizes рюкзак first: This is the backpack...

You could also say:

Это рюкзак, с которым я каждый день хожу в университет.

This gives a little more emphasis to every day.

Or you could rephrase the whole idea:

Я каждый день хожу в университет с этим рюкзаком.

That means:

I go to university with this backpack every day.

This version starts with I, not This is the backpack, so the focus changes.

Not always. With which is the most literal translation, but in natural English we often choose something less formal.

For example:

• Это рюкзак, с которым я хожу в университет каждый день.
  • literal: This is the backpack with which I go to university every day.
  • natural: This is the backpack that I take to university every day.
  • also possible: This is the backpack I go to university with every day.

So when learning Russian, it is useful to understand the literal structure, but you should not feel forced to translate it word-for-word into formal English every time.