This only counts if they recognize you after you return. If they think that you're unique again, then the tracking didn't work at all. This was the case last time I used their tool, Panopticlick.
Edit: I tested this current tool and it recognized me after I returned. Opened it first normally, I'm unique. Opened it in a private window, unique. Closed that and opened a new private window, and bam, one other previous browser had my fingerprint already.
It tells you how much each component contributes lower in the results page. Screen info should be under "Screen Size and Color Depth". For my 2560x1600x24 display 1 in ~1582 have it. The canvas fingerprint was the greatest source for me with 1 in ~2870.
That being said the goal is that the vast majority of users come out unique even if everything is mostly normal individually anyways.
Never was the confirmation that I'm a unique snowflake less welcome.