Meine Nachhilfelehrerin erklärt mir die Grammatik so ruhig, dass ich sie endlich verstehe.

Because Nachhilfelehrerin is a feminine noun, meaning female tutor. In German, the possessive word has to match the noun’s gender, number, and case.

• die Nachhilfelehrerin = the female tutor
• meine Nachhilfelehrerin = my female tutor

If it were a male tutor, you would say:

• mein Nachhilfelehrer

So meine is used here because Nachhilfelehrerin is feminine and in the nominative singular.

It is a compound noun:

• Nachhilfe = tutoring / extra help with schoolwork
• Lehrerin = female teacher

So Nachhilfelehrerin means female tutor or female private teacher.

German often combines words into one long noun, and the last part usually determines the grammatical gender. Since the last part is Lehrerin, the whole noun is feminine.

The verb erklären often takes two objects:

• the person something is explained to → dative
• the thing being explained → accusative

So in this sentence:

• mir = to me → dative
• die Grammatik = the grammar → accusative

A useful pattern is:

• jemandem etwas erklären = to explain something to someone

Examples:

• Sie erklärt mir die Regel. = She explains the rule to me.
• Ich erkläre dir den Satz. = I explain the sentence to you.

Because erklären uses the dative for the person receiving the explanation.

German distinguishes between:

• mich = accusative me
• mir = dative to me / for me

Since the meaning is she explains the grammar to me, German uses mir.

So:

• Sie erklärt mich ... would be wrong here.
• Sie erklärt mir ... is correct.

Here it is accusative singular feminine.

The noun Grammatik is feminine:

• nominative: die Grammatik
• accusative: die Grammatik

For feminine nouns, the article die stays the same in both nominative and accusative, so the form does not change. Its role is shown mainly by the sentence structure and the verb.

In this sentence, die Grammatik is the thing being explained, so it is the direct object.

Here ruhig is not an adjective directly describing a noun. It is being used adverbially, describing how she explains.

• eine ruhige Lehrerin = a calm tutor
  → adjective before a noun, so it gets an ending
• Sie erklärt so ruhig = she explains so calmly
  → adverb-like use, so no ending

This is very common in German: the same word can often be used as an adjective or as an adverb, and adverbs usually do not take endings.

So ... dass means so ... that.

It introduces a result clause: the first part gives the cause or manner, and the dass clause gives the result.

In this sentence:

• so ruhig = so calmly / so quietly
• dass ich sie endlich verstehe = that I finally understand it

So the idea is: She explains the grammar so calmly that I finally understand it.

Other examples:

• Er spricht so schnell, dass ich nichts verstehe.
  = He speaks so fast that I understand nothing.
• Sie war so müde, dass sie einschlief.
  = She was so tired that she fell asleep.

Because dass is a subordinating conjunction, and subordinating conjunctions send the conjugated verb to the end of the clause.

Main clause:

• Meine Nachhilfelehrerin erklärt mir die Grammatik so ruhig

Subordinate clause:

• dass ich sie endlich verstehe

In the dass clause, the verb verstehe comes last.

This is one of the most important German word-order rules:

• main clause: verb usually in second position
• subordinate clause with dass: verb usually at the end

Here sie refers to die Grammatik.

Why? Because Grammatik is a feminine noun, and the accusative pronoun for a feminine singular noun is sie.

So:

• die Grammatik → sie

That gives:

• Ich verstehe die Grammatik.
• Ich verstehe sie.

A learner might notice that Nachhilfelehrerin is also feminine, so in theory sie could look ambiguous. But in context, the sentence clearly means I finally understand the grammar, not I finally understand my tutor.

Endlich means finally, and in this subordinate clause it appears before the verb because the verb must come at the end.

So the order is:

• dass ich sie endlich verstehe

You can think of it as:

• subject: ich
• object: sie
• adverb: endlich
• verb: verstehe

German often places time/manner/focus words like endlich before the final verb in subordinate clauses.

Not with the same meaning.

• so ... dass = so ... that → expresses a result
• weil = because → expresses a reason

Your sentence means:

• She explains it so calmly, with the result that I finally understand it.

If you used weil, the logic would change:

• Meine Nachhilfelehrerin erklärt mir die Grammatik so ruhig, weil ich sie endlich verstehe.

That would mean:

• My tutor explains the grammar so calmly because I finally understand it.

That is a different idea and sounds less natural in this context.

In a normal German main clause, the finite verb goes in second position.

The first position here is occupied by the subject:

• Meine Nachhilfelehrerin

Then the verb comes second:

• erklärt

So the structure is:

• Meine Nachhilfelehrerin | erklärt | mir die Grammatik so ruhig, ...

German calls this the V2 rule (verb-second).

You could also move another element to the front, but then the verb still stays second:

• So ruhig erklärt mir meine Nachhilfelehrerin die Grammatik, dass ich sie endlich verstehe.

That is less neutral, but still follows the same rule.

In this sentence, calmly is usually the better translation.

Ruhig can mean several related things depending on context:

• calm
• quietly
• peacefully
• steady / relaxed

When someone explains grammar, ruhig usually suggests a calm, patient, unhurried way of speaking, not just low volume. So calmly often captures the meaning best.

German pronouns match the grammatical gender of the noun they replace, not just natural gender or the English idea of it.

Since Grammatik is feminine, German uses sie, not a special neutral word.

Compare:

• das Buch → ich lese es
  (Buch is neuter, so es)
• die Grammatik → ich verstehe sie
  (Grammatik is feminine, so sie)

So English it can become er, sie, or es in German, depending on the noun’s gender.

Yes. The German present tense (Präsens) can cover both:

• something happening right now
• something that happens regularly
• a more general present fact

So Meine Nachhilfelehrerin erklärt mir die Grammatik so ruhig, dass ich sie endlich verstehe can mean something like:

• She is explaining the grammar so calmly that I finally understand it.
• My tutor explains grammar to me so calmly that I finally understand it.

The exact meaning depends on context. German uses the present tense more broadly than English sometimes does.