They mean what they would mean in common english.

Specificity because "how specific is the test? Does it measure the true positives correctly without getting a whole heap of false positives as well?" You might ask someone to be "more specific" about something so they aren't including irrelevant things in their discussion.

Sensitivity because "how sensitive is the test? Does it detect the needle in the haystack you need to find? How many does it miss." In common english you might complain that your car brakes are too sensitive - they are too quick to register the pressure from your foot.

Don't forget these are actually strict mathematical concepts. Hope this helps clarify :)