Visibility estimates the share of clicks your site gets from your tracked keywords, compared with ranking first for all of them. It uses typical click rates for each position, so a keyword at position 1 counts far more than one at position 9, and positions beyond the first pages count almost nothing.
The Visibility, last 30 days chart shows the trend. It rises when your keywords move up, and it also changes when you add or remove keywords, so compare periods with the same keyword list.