هذه القضية مهمة.

Because this is a nominal sentence in Arabic. In the present tense, Arabic usually does not use a separate word for is / am / are.

So:

• هذه القضية مهمة = This issue is important

There is no present-tense copula here. Arabic simply places the subject and the predicate next to each other.

If you wanted a past or future meaning, Arabic would use other words, for example:

• كانت القضية مهمة = The issue was important
• ستكون القضية مهمة = The issue will be important

هذه means this for a feminine singular noun.

Arabic demonstratives change according to gender:

• هذا = this (masculine)
• هذه = this (feminine)

The noun القضية is feminine, so Arabic uses هذه:

• هذه القضية = this issue / this case

If the noun were masculine, you would use هذا instead.

A big clue is the ending ـة (called tāʾ marbūṭa), which very often marks a feminine noun.

So:

• قضية = a feminine noun
• therefore it takes feminine agreement:
  • هذه
  • مهمة

That said, not every feminine noun ends in ـة, and not every noun ending pattern tells the whole story by itself, but here the feminine marking is very straightforward.

Because adjectives in Arabic must agree with the noun they describe in:

• gender
• number
• definiteness
• case

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

• مهم = important (masculine singular)
• مهمة = important (feminine singular)

So:

• القضية مهمة = The issue is important

If the noun were masculine, you would say something like:

• هذا الأمر مهم = This matter is important

This is a very common question.

In this sentence, القضية is the subject, and مهمة is the predicate adjective. In Arabic nominal sentences, the predicate is often indefinite, even when the subject is definite.

So:

• القضية = the issue
• مهمة = important

Together:

• القضية مهمة = The issue is important

If you made both words definite:

• القضية المهمة

that would usually mean:

• the important issue

So the difference is:

• القضية مهمة = a full sentence
• القضية المهمة = a noun phrase

In beginner explanations, it is often easiest to understand هذه القضية as one unit meaning this issue.

So the sentence breaks down naturally as:

• هذه القضية = this issue
• مهمة = important

Whole sentence:

• هذه القضية مهمة = This issue is important

In more advanced grammar, Arabic grammarians may analyze the structure more precisely, but for most learners it is perfectly useful to treat هذه القضية as the subject phrase.

A common pronunciation is:

• hādhihi al-qaḍiyya muhimma

If you include full case endings in careful formal reading, it would be:

• hādhihi al-qaḍiyyatu muhimmatun

A few useful notes:

• هذه = hādhihi
• ق in القضية is a deep q sound, not an English k
• ض is an emphatic consonant, often difficult for beginners
• مهمة has a doubled m sound in careful pronunciation: muhimmah

In normal spoken reading, final case vowels are often not pronounced.

الـ is the Arabic definite article, equivalent to the.

So:

• قضية = an issue / a case
• القضية = the issue / the case

In this sentence, the phrase هذه القضية is definite anyway because it means this issue, but Arabic still normally keeps الـ on the noun after a demonstrative in standard usage:

• هذه القضية = this issue

That is the normal MSA pattern.

In standard Arabic, the demonstrative usually comes before the noun:

• هذه القضية = this issue

This is different from English word order, but it is the normal pattern in MSA.

You may sometimes encounter other patterns in dialects or in special styles, but for Modern Standard Arabic, demonstrative + noun is the form to learn first.

Not exactly in the usual descriptive sense.

Compare these two:

• القضية المهمة = the important issue
  Here مهمة is an adjective describing the noun inside a noun phrase.

• القضية مهمة = The issue is important
  Here مهمة is the predicate of the sentence.

So although مهمة is an adjective in form, in this sentence it functions as the predicate: it tells you something about the subject.

That is why the sentence means The issue is important, not the important issue.

Yes. Both the demonstrative and the adjective would change to match a masculine singular noun.

For example:

• هذا الموضوع مهم = This topic is important

Compare:

• هذه القضية مهمة = feminine
• هذا الموضوع مهم = masculine

So Arabic agreement affects multiple words in the sentence, not just one.

Yes, in fully vocalized formal Arabic, this sentence would normally have nominative endings because both the subject and the predicate are nominative in this kind of simple sentence:

• هذه القضيةُ مهمةٌ

More fully transliterated:

• hādhihi al-qaḍiyyatu muhimmatun

But in ordinary Arabic writing, short vowels and tanwīn are usually omitted, so you normally see:

• هذه القضية مهمة

Learners should know the endings exist, but they are often invisible in regular text.

It commonly means something like:

• issue
• case
• matter
• sometimes cause or legal case, depending on context

So هذه القضية مهمة could mean:

• This issue is important
• This case is important

The exact English translation depends on context, but the Arabic grammar stays the same.