Here's the best I can do. Hopefully it helps more than hurts, and that others with greater knowledge can correct its deficiencies.
I went back over the example to see what was what. This passage is in Mounce's Reader as one of the exercises.
I have always taken this marking to indicate an adjective which has a verbal sense. ἐκλεκτοῖς is an adjective meaning essentially "chosen". But one can ask chosen by whom ? You could say there is a choosing action, a verbal sense, present in this adjective, which is in fact brought out directly in verse 2 - κατὰ πρόγνωσιν θεοῦ πατρὸς - "according to the foreknowledge of God the Father". There is a cognate verb in Greek εκλεγω, (εκλεγομαι in the NT) meaning basically to choose or select. You could contrast this with something like "to the red" where "red" while adjectival is not verbal in any meaningful way.
The problem with looking up "verbal adjective" in Greek grammars (eg. in Acc via Search All) is that you immediately end up in the middle of participles which are not quite the same thing, though I could imagine a participle being used similarly.