What is the meaning of auditory in following sentence Scientists have studied effects aging on abilities elderly.?

The sentence you provided, "Scientists have studied effects aging on abilities elderly," is missing the word "auditory". To give you the meaning of "auditory" in that sentence, I'll assume you meant:

"Scientists have studied the effects of aging on auditory abilities in the elderly."

In this sentence, "auditory" refers to the sense of hearing.

Therefore, the sentence is about how scientists have investigated how the process of aging affects the hearing abilities of older people.