Auffassungsgabe can be translated to many things: readiness of mind, comprehension or grasp, to name some. If you separate the words it consists of you get Auffassung (view, opinion, conception) and Gabe (gift).

Auffassung has its roots in the German verb fassen, which means to receive or take something, in this case information. Gabe has its roots in the Old High German word gëban, which can to bring or give something to somebody (like a gift). Hence it is the gift to process views, opinions or conceptions.

In German, it is usually used to describe people with a quick wit, those people that are able to get information and to immediately process it. Therefore, the people who can do this rather quickly have an advantage.

An example: At university, after a complicated lecture, the professor might ask if there are any questions. Most of the time, nobody raises their hands. That is because their minds need some more time to thoroughly process the given information before being ready to ask a question about the topic.

Sometimes, though, there might be that one person who always raises their hand first. That person seems to have a schnelle Auffassungsgabe (a quick understanding of the information’s context).

On the other hand, if you are with a person who always seems to see every little detail (“Look at that tiny red dot on the billboard across the street. Do you think that has a meaning?”), you can also speak of a rather well working Auffassungsgabe.

Examples:

Peter hat eine etwas bessere Auffassungsgabe als sein Cousin.

Peter has a quicker perception than his cousin.

Sie hat eine schnelle Auffassungsgabe.

Her readiness of mind is rather quick.