Learn Hardcore Russian: Ты же знаешь, что сегодня у нас встреча. - You do know that we have a meeting today.

Ты знаешь, что сегодня у нас встреча.
= You know that we have a meeting today. (neutral statement)
Ты же знаешь, что сегодня у нас встреча.
≈ You *do know we have a meeting today / You already know we have a meeting today / You remember we have a meeting today, right?*

Typical nuances of же here:

reminding someone of something they already know
mild reproach or impatience (Come on, you know this!)
appealing to shared knowledge (As you know…)

So же is like adding already, after all, or a slightly reproachful you know in English, depending on tone.

Can I just leave out же? Will the sentence still be correct?

Yes, you can.

Ты знаешь, что сегодня у нас встреча. – fully correct, neutral.
Ты же знаешь, что сегодня у нас встреча. – also correct, but more emotionally colored (reminder / mild reproach / emphasis).

Without же, you sound more matter‑of‑fact. With же, you sound as if:

you’re sure the other person already has this information, or
you’re slightly surprised they might be forgetting it.

What exactly does что mean here? Is it the same что as in the question Что? (“What?”)?

Here что is a conjunction, not a question word.

Question word: Что? = What?
Conjunction: что = that (introducing a subordinate clause)

In Ты же знаешь, что сегодня у нас встреча:

Ты (же) знаешь – main clause: You (do) know
что сегодня у нас встреча – subordinate clause: that we have a meeting today

In English, we often drop that:

You know (that) we have a meeting today.

In Russian, you normally keep что in this kind of sentence.

Why is there a comma before что?

Because что introduces a subordinate clause (an object clause).

Structure:

Main clause: Ты же знаешь, …
Subordinate clause: что сегодня у нас встреча.

Russian punctuation rules require a comma between these two clauses: Ты же знаешь, что…

What does у нас встреча literally mean, and why is there no verb “to have” like in English?

Literally:

у = at / by / with (here: a preposition used with the genitive)
нас = of us (genitive of мы)
встреча = a meeting

So у нас встреча is literally “(there is) a meeting at us”, which is how Russian often expresses “we have a meeting”.

Russian usually avoids a direct verb “to have” in this sense. Instead it uses:

у + [person in genitive] + [noun]
у нас встреча = We have a meeting
у меня книга = I have a book
у него машина = He has a car

Where is the verb “is” or “have” in у нас встреча? Why isn’t it есть?

There is an “understood” verb есть (there is / there exists), but it is usually omitted when:

the existence is obvious, or
you talk about a specific, known thing (like a scheduled meeting).

So:

У нас есть встреча. – We have a meeting (there exists such a thing; more about the fact of having it).
У нас встреча. – We (are having) a meeting / We have a meeting (on schedule, more concrete and immediate).

In your sentence, Ты же знаешь, что сегодня у нас встреча, есть would sound unnecessary and a bit heavy. The short form is more natural in everyday speech.

Would Ты же знаешь, что сегодня у нас есть встреча be wrong?

It’s grammatically correct, but stylistically it sounds less natural in this context.

Ты же знаешь, что сегодня у нас встреча.
→ natural reminder of a specific, scheduled event.
Ты же знаешь, что сегодня у нас есть встреча.
→ puts slightly more emphasis on the fact of having a meeting as a kind of item we “possess”; it can sound more formal or bookish here, and less like casual spoken Russian.

Speakers almost always drop есть in a sentence like this.

What case is нас in, and why?

нас is in the genitive case.

The preposition у (in the “have”-construction) always takes the genitive:

у меня (of me) – I have
у тебя (of you, informal) – you have
у него / у неё – he/she has
у нас – we have
у вас – you have (formal/plural)
у них – they have

So у нас встреча = there is a meeting at/with us → we have a meeting.

Why is встреча in the nominative case? Shouldn’t something be in genitive after у?

Only the person after у is in the genitive (у нас).

The thing that is “had” (the meeting) is the logical subject of this existential construction and stays in the nominative:

у нас встреча – we have a meeting (literally: at‑us [is] a meeting)
у меня книга – I have a book
у него проблема – he has a problem

So the pattern is:

у + [person in genitive] + [thing in nominative]

How would I make this sentence polite/formal, using Вы instead of Ты?

Change the pronoun and verb form:

Informal: Ты же знаешь, что сегодня у нас встреча.
Formal or plural: Вы же знаете, что сегодня у нас встреча.

Differences:

ты → вы
знаешь (2nd person singular) → знаете (2nd person plural/formal)

Does Ты же знаешь… sound rude? Is there a negative feeling in же?

It depends on intonation and context.

Possible shades:

Neutral reminder: You remember that we have a meeting today, right?
Gentle reproach: Come on, you know we have a meeting today.
Stronger irritation (with sharp tone): You *do know we have a meeting today!* (implying “why are you acting like you don’t?”)

By itself, же is not rude; it’s just an emotional particle. It becomes more or less sharp depending on how you say it.

Could I use ведь instead of же here? What’s the difference between Ты же знаешь and Ты ведь знаешь?

Yes, you can:

Ты же знаешь, что сегодня у нас встреча.
Ты ведь знаешь, что сегодня у нас встреча.

Both can be translated as:

You do know that we have a meeting today.
After all, you know we have a meeting today.

Differences in feel (subtle):

же is very common and can sound a bit more immediate, sometimes slightly sharper.
ведь often sounds a bit more explanatory or persuasive, like “You know (after all)… / You know, don’t you, because…”

But in many everyday situations they overlap and either would be understood the same way.

Can I change the word order, like У нас сегодня встреча or Сегодня встреча у нас? Does it change the meaning?

All of these are grammatically correct; they differ in emphasis:

Сегодня у нас встреча.
Neutral, common: Today we have a meeting.
Slight focus on today as the time frame.
У нас сегодня встреча.
Very similar, maybe a tiny emphasis on we (we have a meeting today).
Сегодня встреча у нас.
Emphasizes у нас (with us / at our place), as opposed to someone else:
The meeting today is *with us / at our place.*

In your full sentence:

Ты же знаешь, что сегодня у нас встреча. – most natural, neutral option.

How is this sentence usually pronounced? Where is the stress?

Stresses in the individual words:

ты́ – stress on ы
же – unstressed (clitic)
зна́ешь – stress on зна́
что́ – stress on о́
сего́дня – stress on го́: се‑го́д‑ня
у нас – нас stressed if you emphasize “we”
встреча – встреча́ (stress on ча́)

A neutral intonation would usually rise slightly on знаешь, then fall over the rest:

Ты́ же зна́ешь, что сего́дня у нас встре́ча.

What would be a natural English translation that captures the nuance of же?

Depending on context and tone, good options include:

You *do know we have a meeting today.*
You *know we have a meeting today, right?*
You *remember we have a meeting today.*
But you *know we have a meeting today.*

All of these try to express the reminder / shared knowledge nuance that же adds.