هذه القيمة مهمة.

Because القيمة is a feminine singular noun in Arabic, and the demonstrative must match it.

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

So:

• هذا الكتاب = this book
• هذه القيمة = this value

Even though an English noun may not feel “feminine,” Arabic nouns have grammatical gender, and قيمة is feminine.

In standard Arabic, when you say this + noun, the noun is usually definite, so it normally takes الـ.

So the usual pattern is:

• هذا الكتاب
• هذه السيارة
• هذه القيمة

Literally, Arabic uses something closer to this the-value, but in natural English we just say this value.

If you said هذه قيمة, that would usually not mean the same thing as the basic this value structure.

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

So:

• هذه القيمة مهمة literally looks like:
• this value important

But it means:

• This value is important

This is very normal in Arabic. If you want the past or future, then Arabic does use verbs:

• كانت هذه القيمة مهمة = This value was important
• ستكون هذه القيمة مهمة = This value will be important

Because مهمة describes القيمة, and adjectives in Arabic usually agree with the noun they describe in:

• gender
• number
• definiteness
• case

Since القيمة is feminine singular, the adjective must also be feminine singular:

• masculine: مهم
• feminine: مهمة

So:

• كتاب مهم = an important book
• قيمة مهمة = an important value

Good question. Here مهمة is not just an ordinary adjective inside a noun phrase; it is the predicate of the sentence.

The structure is:

• هذه القيمة = the subject: this value
• مهمة = the predicate: important

So the sentence means:

• This value is important

In this kind of sentence, the predicate is often indefinite, so مهمة appears without الـ.

Compare:

• القيمة المهمة = the important value
  Here المهمة is part of the noun phrase and must be definite.

But:

• القيمة مهمة = the value is important
  Here مهمة is the predicate, so it does not need الـ.

It is a nominal sentence (جملة اسمية) in Arabic.

You can break it down like this:

• هذه القيمة = subject-like part (this value)
• مهمة = predicate (important)

More traditionally:

• هذه = demonstrative
• القيمة = noun being pointed to
• together they function as the topic/subject
• مهمة = predicate/comment about that subject

So the sentence is a very typical Arabic pattern:

• [noun phrase] + [predicate]

The final ة is called tāʾ marbūṭa.

In normal pause pronunciation (for example, at the end of a word or sentence), it usually sounds like -a or -ah, not a clear t.

So you will often hear:

• القيمة ≈ al-qīmah
• مهمة ≈ muhimmah

But when grammar endings are fully pronounced, or when the word is connected in certain contexts, the t sound can appear more clearly.

For a learner, a good practical pronunciation is:

• hādhihi al-qīmah muhimmah

With full case endings, it would be:

هَذِهِ القِيمَةُ مُهِمَّةٌ

Here:

• هَذِهِ = fixed demonstrative form
• القِيمَةُ = nominative
• مُهِمَّةٌ = nominative

Why nominative? Because in this nominal sentence:

• the subject part is nominative
• the predicate is also nominative

In everyday printed Arabic, these endings are usually not written, so you normally see:

هذه القيمة مهمة

Yes. هذه and القيمة go together as one noun phrase:

• هذه = this
• القيمة = the value
• together: this value

Then مهمة tells you something about that phrase.

So the sentence divides naturally into:

• هذه القيمة / مهمة
• this value / is important

This is a useful pattern to recognize, because you can make many similar sentences:

• هذه الفكرة جديدة = This idea is new
• هذه المشكلة كبيرة = This problem is big
• هذه الكلمة صعبة = This word is difficult

Yes. Depending on context, قيمة can mean things like:

• value
• worth
• importance
• sometimes price or numerical value

So هذه القيمة مهمة could be used in different situations, such as:

• mathematics
• economics
• ethics
• general discussion

The exact nuance depends on context, even though the grammar stays the same.