A more direct or literal translation of Geschicklichkeit would probably be something like or skilledness or skillfulness. Other words with the -lichkeit ending that might be more familiar are Freundlichkeit (friendliness) and Brüderlichkeit (brotherliness)
(So there are actually two endings here. -lich is cognate to english -ly, though -ed can also work. -keit is equivalent to english -ness)
The base word, Geschick, translates to ‘skill’ on its own. The difference is that it strictly (edit: apparently not) behaves as a countable noun, as in you can have a number of skills, just as you can have a number of friends, of brothers, etc. It doesn’t work when describing a quality or property someone may possess, so that’s where the suffixes come in.
It’s the difference between “there’s a lot of friend here” and “there’s a lot of friendliness here”
In English, skill is an exception to a rule. It can be used in both ways, without the help of suffixes. German, on the other hand, doesn’t generally make that kind of exception in the interest of maintaining consistency. edit: seems this exception is actually a similarity between English and German, though perhaps German slightly prefers the longer form in cases such as this one.
The Germans are probably going to roast me for this but that’s my understanding from just under 2 years of learning and a brief series of googles.