noun

• (informal) Surveillance.
  "Intelligence work is necessarily limited in scope by the capacity of national surveillance systems. […] Ultimately, it is only when you have an 'eyeball' or the electronic equivalent on a suspect that you have a reasonable chance of a preventive intervention."
• (marketing, in the plural) A readership or viewership.
  "We need compelling content for the new Web site so we can attract more eyeballs."
• (CB radio, slang) A face-to-face meeting.
  "We had an eyeball last year."
• (Caribbean) A favourite or pet; the apple of someone's eye.

verb

• (transitive, informal) To gauge, estimate or judge by eye, rather than measuring precisely; to look or glance at.
  "A good cook can often just eyeball the correct quantities of ingredients."
• (transitive, informal) To stare at intently.
  "Are you eyeballing my girl?"
• (intransitive) To roll one's eyes.
  "Guardiola strode on to the pitch at half-time to remonstrate with the Spanish referee, Antonio Mateu Lahoz, but went too far with his eyeballing and matador-like hand movements. He was “upstairs”, in the Colin Bell stand, to watch Liverpool’s second-half turnaround and a dismal seven days for City take another turn for the worse."