No hables tan deprisa, que no te entiendo.

Because this is a negative command: No hables... = Don't speak...

In Spanish, negative commands for tú use the present subjunctive, not the normal present tense.

• hablas = you speak / you are speaking
• hables = the form used in No hables = don't speak

So:

• Hablas muy deprisa. = You speak very fast.
• No hables tan deprisa. = Don't speak so fast.

It is a command/request, not a statement.

A statement with tú would be:

• No hablas = You don't speak

But here we have:

• No hables = Don't speak

That difference is very important in Spanish:

• hablas = indicative, normal statement
• hables = subjunctive form used in a negative command

Here tan means so.

So tan deprisa means so fast.

That is different from muy, which means very:

• muy deprisa = very fast
• tan deprisa = so fast

In this sentence, tan fits especially well because it is followed by a consequence/explanation:

• No hables tan deprisa, que no te entiendo.
• Literally: Don't speak so fast, that/because I can't understand you.

A very common Spanish pattern is:

• tan + adjective/adverb + que

For example:

• Habla tan bajo que no oigo nada. = He speaks so quietly that I can't hear anything.

Deprisa means quickly / fast.

Yes, you can often say rápido instead in everyday Spanish:

• No hables tan deprisa.
• No hables tan rápido.

Both sound natural.

A few notes:

• deprisa is an adverb
• rápidamente is also an adverb, but sounds a bit more formal or careful
• rápido is very common in speech, even though it is originally an adjective

In Spain, deprisa is very common and natural.

Here que introduces the reason or consequence: I can't understand you.

So the sentence means something like:

• Don't speak so fast, because I can't understand you.
• or Don't speak so fast, I can't understand you.

This use of que is very common in spoken and informal Spanish. It can sound more direct and natural than always using porque.

So:

• No hables tan deprisa, que no te entiendo.

is a very natural way to say:

• Don't speak so fast, I can't understand you.

Yes, the comma matters a little.

With the comma:

• No hables tan deprisa, que no te entiendo.

the second part sounds more like an added explanation: Don't speak so fast, because I can't understand you.

Without the comma:

• No hables tan deprisa que no te entiendo.

it feels more tightly linked as so fast that I can't understand you.

In real life, both ideas are very close. The version with the comma matches a natural pause in speech and is very common in this kind of request.

Te means you.

More exactly, it is the direct object pronoun for tú.

• entiendo = I understand
• te entiendo = I understand you
• no te entiendo = I don't understand you

In Spanish, object pronouns usually come before a normal conjugated verb:

• Te veo. = I see you.
• Te escucho. = I hear/listen to you.
• No te entiendo. = I don't understand you.

Yes. No hables is the tú form, so the speaker is talking to one person informally.

In Spain, the other common possibilities are:

• usted: No hable tan deprisa, que no le entiendo.
• vosotros: No habléis tan deprisa, que no os entiendo.
• ustedes: No hablen tan deprisa, que no les entiendo.

So the original sentence is informal singular: you = one person you know, a friend, classmate, child, etc.

Yes, it is natural in Spain.

Especially Spanish-from-Spain learners should notice that deprisa is very normal there.

Other natural ways to say something similar are:

• Habla más despacio, por favor. = Speak more slowly, please.
• No hables tan rápido.
• ¿Puedes hablar más despacio? = Can you speak more slowly?

The original sentence sounds direct but perfectly normal. If you want to sound softer or more polite, asking with ¿Puedes...? or adding por favor is common.

A simple approximation is:

• hables ≈ AH-bles
• deprisa ≈ deh-PREE-sa

A few useful pronunciation points:

• The h in hables is silent
• hables is stressed on the first syllable: HA-bles
• deprisa is stressed on pri: de-PRI-sa
• The r in deprisa is a single tapped r, not a strong rolled rr

So the full sentence is roughly:

• No AH-bles tan deh-PREE-sa, ke no te en-TYEN-do.

That is only an approximation, but it can help at first.