هذا الدرس جديد، لكنني أفهمه جيدا.

Because درس is a masculine singular noun in Arabic, and هذا is the masculine singular form of this.

• هذا الدرس = this lesson
• هذه السيارة = this car

So the demonstrative has to match the noun’s gender and number.

In Arabic, when this/that directly modifies a noun, the noun is usually definite too.

So:

• هذا الدرس = this lesson
• هذا الكتاب = this book

If you say هذا درس, that usually means this is a lesson, not this lesson.

This is a very common difference from English.

Because in Modern Standard Arabic, the present-tense verb to be is usually not expressed in sentences like this.

So Arabic says:

• هذا الدرس جديد

Literally: this lesson new

But the natural English meaning is:

• This lesson is new

This kind of sentence is called a nominal sentence.

In Arabic, adjectives normally come after the noun.

But there is also an important structure point here:

• الدرس الجديد = the new lesson
• الدرس جديد = the lesson is new

So in your sentence, جديد is not just an adjective inside the noun phrase. It is the predicate: it tells you something about الدرس.

Because جديد here is a predicate, not a definite adjective attached directly to الدرس.

Compare:

• هذا الدرس جديد = This lesson is new
• هذا الدرس الجديد = This new lesson

In هذا الدرس الجديد, the adjective is part of the noun phrase, so it must be definite too. In هذا الدرس جديد, جديد is the statement about the lesson, so it stays indefinite.

لكنني means but I or but as for me.

It is built from لكن meaning but, plus a first-person element. In fully vocalized writing, you may see لكنَّني, and you may also encounter لكني.

A useful point for learners:

• Do not read -ني here as the object me of أفهم
• The verb is still أفهم = I understand

So the overall idea is simply but I...

Because Arabic present-tense verbs mark the subject with prefixes.

Here, the prefix أ- marks first-person singular:

• أفهم = I understand
• تفهم = you understand / she understands
• يفهم = he understands

So the subject I is already built into the verb.

Because Arabic commonly attaches object pronouns directly to verbs.

• أفهم = I understand
• أفهمه = I understand it

The ending -ه is a masculine singular object pronoun. It refers back to الدرس.

Yes. -ه can mean him or it, depending on the noun it refers to.

In this sentence, it means it, because it refers to الدرس.

So:

• أفهمه = I understand it

Yes, that is grammatically correct.

But أنا is usually unnecessary here, because أفهم already means I understand.

So:

• أفهمه جيدا = I understand it well
• أنا أفهمه جيدا = I understand it well, with extra emphasis on I

In your sentence, لكنني already gives a clear but I, so a separate أنا would usually only be used for stronger emphasis.

The basic word جيد means good as an adjective.

But جيدًا is often used adverbially, so it means well:

• كتاب جيد = a good book
• أفهمه جيدًا = I understand it well

So in your sentence, جيدا modifies the verb أفهم, not the noun الدرس.

In fully vocalized Arabic, it is written جيدًا. That ending includes tanwīn fatḥ, and Arabic spelling often adds a supporting alif at the end for this -an ending.

So you may think of it like this:

• unvowelled: جيدا
• fully vocalized: جيدًا

That final ا is mainly a spelling convention.

Because د is a sun letter.

When الـ comes before a sun letter, the l sound assimilates to the next consonant in pronunciation.

So:

• written: الدرس
• pronounced: roughly ad-dars

The spelling does not change, only the pronunciation does.

A fully vocalized version is:

هٰذا الدرسُ جديدٌ، لكنَّني أفهمه جيدًا.

If you are learning case endings, the main points are:

• الدرسُ is nominative
• جديدٌ is also nominative, because it is the predicate
• جيدًا is accusative/adverbial

In normal everyday Arabic writing, these short vowels are usually left out.