I was reading an article which title is "Oral health of persons with and without dementia attending a geriatric clinic." when i realized i don't understand what it means.Is it a way to evoke a medical exam or the waiting time for an hospitalisation?

I would say the article was perhaps not written by a native speaker of English, as one does not "attend" a clinic. One goes there, or visits one....so the 'attending' part is confusing.

I would say the title means "This article talks about the health of old people's mouths -- regardless of if they are still mentally clear or not. The research was done in a clinic that cares exclusively for old people."