هذا كيس النفايات.

• هذا = this
• كيس = bag
• النفايات = the trash / the garbage / the waste

Together, كيس النفايات is literally bag of the trash, which is the normal Arabic way to express trash bag or garbage bag.

It can be understood either way, depending on context.

• As a full sentence, it means This is the trash bag.
• In context, it can also function like this trash bag.

That is common in Arabic with demonstratives like هذا. Context usually makes the intended reading clear.

In Arabic, the present-tense verb to be is usually omitted in simple nominal sentences.

So Arabic says:

• هذا كيس النفايات

but English naturally says:

• This is the trash bag

The idea of is is understood without being spoken.

Because كيس is masculine singular, and هذا is the masculine singular word for this.

Arabic agreement follows the main noun, which here is كيس, not النفايات.

So:

• هذا كيس = this bag
• هذه حقيبة = this handbag / this purse

It is an iḍāfa construction, often called a genitive construct or noun-to-noun phrase.

In an iḍāfa:

• the first noun is the main thing: كيس = bag
• the second noun specifies it: النفايات = trash

So كيس النفايات literally means bag of the trash, which English usually expresses as trash bag.

Arabic often uses this structure where English uses of or turns one noun into an adjective-like word.

Because in an iḍāfa, the first noun normally does not take الـ.

So Arabic says:

• كيس النفايات

not:

• الكيس النفايات

The definiteness of the whole phrase comes from the second noun, النفايات, which does have الـ.

For the same reason: in an iḍāfa, the first noun does not take tanween.

So in fully vocalized Arabic, this would be:

• كيسُ النفاياتِ

not:

• كيسٌ النفاياتِ

That is a very common rule learners need to get used to.

Arabic often uses الـ with words that are generic or class-level in meaning.

Also, in an iḍāfa, making the second noun definite makes the whole phrase definite. So كيس النفايات becomes a definite expression.

This does not always match English article usage perfectly. Arabic and English do not divide definiteness in exactly the same way.

It is written with الـ, but because ن is a sun letter, the l sound of الـ is not pronounced.

So النفايات is pronounced roughly:

• an-nifāyāt

not:

• al-nifāyāt

So the whole sentence is roughly:

• hādhā kīs an-nifāyāt

If you read it as a standalone sentence in careful MSA, it would commonly be:

• هذا كيسُ النفاياتِ

Here:

• كيسُ is nominative
• النفاياتِ is genitive because it is the second part of the iḍāfa

In normal pauses, and in most everyday reading and speech, those final short vowels are often not pronounced.

It is plural. Its singular form is نفاية.

Arabic often uses a plural word where English uses an uncountable noun like trash, garbage, or waste.

Even though النفايات is plural, the demonstrative is still هذا, because the main noun being pointed to is كيس, and كيس is masculine singular.