Getting Definite About Definiteness In Arabic

The definite article al (ال) is incredibly important in Arabic grammar. It is used in a variety of grammatical constructs and the omission or addition of al can change the meaning of a sentence.

Note: al corresponds to the article "the" in English in that al can make a word definite.

For example:

•  الفيل الكبير
• The big elephant
• الفيل كبير
• The elephant is big

In nominative sentences (sentences without a verb), al 

In an iDaafa (إضافة), Arabic's possessive construct, the very last item must have al attached to it if the iDaafa is to be definite [unless the last item is a possessive pronoun].

• اسم المدرس
• The name of the teacher 
•  صحفي جريدة حكومة العراق
• The journalist of the newspaper of the government of Iraq 
• صديقي
• My friend

I've thrown the word definite around a lot so far, but if al is the definite article why do sentences like:

• القرود مجنون
• Monkeys are crazy

translate into indefinite sentences in English?

The reason is because al can also attach to a word to refer to that word in a general sense. 

Like:

•  أحب الجبن
• I like cheese

 So it might be easier to think of al as having the ability to both identify something specific and to refer to something in the general sense.

Another, lesser used meaning of al is as a synonym for kull (كل), which translates to "all" or "every" depending on if the word following it is definite or indefinite, respectively. 

Famous example from Surat al-fatiHa (The opening chapter of the Qur'an):

• الحمد لله رب العالمين
• All praise is due to Allah (God), Lord of the worlds

Note: Some translations also translate العالمين as "All of the worlds"

Finally, al is very important when used with a maSdar (مصدر, it literally means "source"), which roughly corresponds to gerunds and infinitives in English.

• أريد الذهاب إلى بيتك
• I want to go to your house
• هل أستطيع مساعدتك؟
• Can I help you?

Note the idiomatic use of an iDaafa to convey the meaning. Literally, the second sentence translates to: [Question Particle] Can I helping of you?

Also note that ال + مصدر can be replaced with َأن + فعل ( 'an + the subjunctive verb).

So I could have written: هل أستطيع أنْ أساعدَك؟ with the same meaning as the second sentence.

There are other uses of al not mentioned here, some of which are sometimes used in poetry. 

That's all for now! Feel free to ask for clarifications.