هذه العملية مهمة.

Because العملية is a feminine singular noun, and the demonstrative must match it.

• هذا = this for masculine singular nouns
• هذه = this for feminine singular nouns

So:

• هذا الكتاب = this book
• هذه العملية = this process / this operation

Arabic agreement is stricter than English here: the word for this changes depending on gender.

It is simply a noun that is grammatically feminine in Arabic. One clue is its ending: it ends in ـة (taaʾ marbuuṭa), which very often marks feminine nouns.

So:

• عملية = a feminine noun
• therefore it takes feminine agreement:
  • هذه not هذا
  • مهمة not مهم

As in many languages, grammatical gender does not always mean biological gender. A word like عملية is feminine because that is how the noun behaves grammatically.

Because in Arabic, the present-tense verb to be is usually not stated in simple sentences like this.

So:

• هذه العملية مهمة literally looks like this process important
• but it means This process is important

This kind of sentence is called a nominal sentence in Arabic.

If you want a past or future meaning, Arabic does use verbs:

• كانت هذه العملية مهمة = This process was important
• ستكون هذه العملية مهمة = This process will be important

But in the present, no separate word for is is needed.

Because مهمة is an adjective describing العملية, and Arabic adjectives normally:

1. come after the noun
2. agree with the noun in gender, number, and definiteness

So here:

• العملية = feminine singular, definite
• مهمة = feminine singular

That is why you get:

• العملية مهمة = the process is important

If the noun were masculine, you would use مهم:

• هذا الأمر مهم = This matter is important

That is normal in Arabic. With a demonstrative like هذا / هذه, the following noun is usually also definite.

So Arabic says:

• هذه العملية
• literally something like this the-process

But in natural English, that is just this process.

This is a standard Arabic pattern, not a mistake. The demonstrative and the noun work together as one definite phrase.

العملية can have several meanings depending on context. Common ones include:

• process
• operation
• procedure
• sometimes surgery / surgical operation

So هذه العملية مهمة could mean:

• This process is important
• This operation is important
• This procedure is important

The surrounding context tells you which meaning is intended.

In careful Modern Standard Arabic, it is pronounced approximately:

hādhihi al-ʿamaliyyatu muhimmatun

In normal pause-form pronunciation, learners often hear something closer to:

hādhihi al-ʿamaliyyah muhimmah

A few notes:

• هذه = hādhihi
• العملية contains the consonant ʿayn (ع), which has no exact English equivalent
• the final short case vowels are often not pronounced in everyday reading aloud unless the speaker is using full formal pronunciation

Yes, in fully vocalized formal Arabic there are case endings, although they are often omitted in ordinary writing and often dropped in pause when speaking.

The fully marked sentence is:

هٰذِهِ العَمَلِيَّةُ مُهِمَّةٌ

A grammatical breakdown:

• هٰذِهِ = feminine singular demonstrative
• العَمَلِيَّةُ = subject/topic of the nominal sentence, so it is typically nominative
• مُهِمَّةٌ = predicate, also typically nominative

That is why you may see ـُ / ـٌ in fully vocalized texts. But in most everyday printed Arabic, these endings are not written.

Yes. That would mean:

• العملية مهمة = The process is important

With هذه, you are specifically saying this process:

• هذه العملية مهمة = This process is important

So the difference is mainly whether you want to point out a specific process as this one.

In Modern Standard Arabic, the most standard form is:

هذه العملية مهمة

Putting the demonstrative after the noun, as in العملية هذه, is more associated with spoken varieties of Arabic and is less standard in formal MSA.

So for a learner of Modern Standard Arabic, it is best to use:

• هذه العملية = this process

rather than:

• العملية هذه

It is a full sentence, not just a noun phrase.

• هذه العملية = this process → a noun phrase
• هذه العملية مهمة = This process is important → a complete sentence

The structure is:

• subject/topic: هذه العملية
• predicate/comment: مهمة

So the sentence is making a statement about this process.