It’s entirely possible to understand the meaning of this page without background knowledge on gems because of context clues, but if you care about the terminology, I’ve provided information below:
 
So on this page, I used the GIA Gem Clarity Grading Code.  
A gemstone’s clarity grade indicates the relative absence of inclusions (materials trapped inside the gem), fractures, and blemishes (surface imperfections) that affect its appearance and structural integrity.
 
Coloured gemstones can have the following grades:
 
VVS: very, very small inclusions  
VS: very small inclusions  
SI1 and SI2: small inclusions  
I1, I2, and I3: included  
“Eye clean” (or “eye clear”) means the gem has no evident flaws visible to the unaided eye when viewed from a distance of about 6” to 12”.
 
More info on gem grades can be found here.