Profesoara explică aceeași expresie de două ori, ca să înțelegem sensul ei.

Because profesoara is the definite form: the teacher.

• profesoară = a female teacher
• profesoara = the female teacher

Romanian usually puts the definite article at the end of the noun instead of using a separate word like English the.

Because aceeași has to agree with expresie, which is feminine singular.

• același is used with a masculine singular noun
• aceeași is used with a feminine singular noun

So:

• același cuvânt = the same word
• aceeași expresie = the same expression

It means the same.

In this sentence, aceeași expresie means the same expression. Romanian uses this word very often to show identity: not a similar expression, but exactly the same one.

De două ori means twice.

Literally, it is something like of two times, but you should learn it as a normal Romanian expression for frequency.

Common patterns are:

• o dată = once
• de două ori = twice
• de trei ori = three times

So explică ... de două ori simply means explains ... twice.

Ca să introduces a purpose clause. It means so that or in order to.

So:

• ca să înțelegem sensul ei = so that we understand its meaning

This is a very common and natural Romanian structure.

Yes. After ca să, Romanian normally uses the subjunctive.

Here the subjunctive marker is să:

• înțelegem = we understand
• să înțelegem = that we understand / so that we understand

For we forms, the verb often looks the same as the present indicative, so the important signal is să.

It is built into the verb.

Romanian often drops subject pronouns because the verb ending already shows the person:

• înțeleg = I understand
• înțelegi = you understand
• înțelegem = we understand

So înțelegem already means we understand, without needing noi.

Romanian usually expresses possession here with:

definite noun + possessive word

So:

• sensul = the meaning
• ei = her / its
• sensul ei = its meaning / her meaning

This is the normal Romanian order.

Also, the noun is definite: sensul, not just sens, because Romanian commonly uses the definite form in this kind of possessive structure.

It refers to expresie.

So sensul ei means its meaning, where its = the expression's.

Grammatically, ei can mean her or its, but here the context makes it clear that the teacher is explaining the expression so that we understand the meaning of the expression.

Because that part is a subordinate clause of purpose.

The main clause is:

• Profesoara explică aceeași expresie de două ori

The purpose clause is:

• ca să înțelegem sensul ei

Romanian normally separates this kind of clause with a comma.