This is the 10756th most frequent German word.
roter
"Roter" means "red" (masculine nominative singular or masculine/feminine genitive singular form).
Here, 'roten' is used as an adjective to describe the noun 'Apfel'. It is inflected to match the accusative case and masculine gender.
Ich habe einen roten Apfel gegessen.
I ate a red apple.
In this sentence, 'rote' is used to describe the noun 'Ball', in the nominative case and masculine gender.
Der rote Ball liegt im Garten.
The red ball is lying in the garden.
'roten' is the adjective describing 'Teppich', inflected for the accusative case and masculine gender.