Clear of inclusions and imperfections to the naked eye. That is, an ‘eye-clean’ diamond doesn’t display any blemishes or internal flaws if a jeweler looks at it without a microscope. With a microscope, however, the jeweler may be able to detect inclusions.
The GIA scale considers flawless (FL), internally flawless (IF), very very slightly (VVS), and very slightly included (VS) diamonds eye-clean.
One issue with ‘eye-clear’ comes with buying diamonds online. These may seem visibly clear on one’s screen but not when viewed in person. The best way to avoid this situation when ordering a diamond or an engagement ring online is to work with a reputable jeweler such as Peter Norman.