"a big house and a big car"
Translation:بَيْت كَبير وَسَيّارة كَبيرة
(kabír) is an adjective which follows the noun in all its condition (if it is attributive, that is, describing the noun directly).
Baytun Kabírun, Sayyáratun Kabíratun.
Bayt: masculine noun. It's indefinite, so we add Tanwin to its end (-un) -> Baytun.
Kabírun: Adjective describing "bayt" so it must be indefinite and gets Tanwin at its end. It is also masculine in form.
Sayyárah: Feminine noun ending with Ta Marbútah. Ta' Marbútah changed from "H" to "T" when a vowel is added to it. Since it is indefinite (there is no AL in the beginning of the word) then we have to add Tanwin (-un) -> Sayyáratun.
Kabíratun: Same adjective like before, but here we add Ta-Marbúta too because "Sayyárah" is feminine and the adjective must be feminine. Sayyárah is indefinite and so this adjective must also be indefinite, and we add Tanwin (-un) to it.
Let's make the above sentence definite
البيتُ الكبيرُ والسيارةُ الكبيرةُ
Here I've made everything defined. The sentence becomes: Al-baytu Al-Kabíru, Al-Sayyáratu Al-Kabíratu. (THE big house, THE big car).
We removed the Tanwin because now we added (AL) for "the". Because of that also, the adjective (kabír) gets AL as well.
Hope it is clear this way!
In modern dialects, people now mostly don't care much about the endings. However, the ending vowels have a critical rule in Arabic cases. In "normal" conditions, a noun in nominative case would end with (-u) when the noun is defined (with AL of course), and if it is indefinite that would be (-un).
The accusative case would make the noun end with -a (or -an if indefinite).
Other cases when some preposition comes before the noun or being in Genitive, would place (-i) to the end (or -in for indefinite noun).
This is a brief description and I'm trying to match the names of cases as much as possible (we study Arabic in a completely different scheme and names). Things change when nouns are in dual case or plural case, and some nouns are simply irregular so they need special treatment ...etc