In British English this is often just a posh or old-fashioned way to say very. I’m frightfully sorry means I’m very sorry; that’s frightfully kind means that’s very kind. It has almost nothing to do with being scared any more. Older speakers, and people putting on a posh voice, use it more; younger people may use it for fun, as if they were in an old film. Americans hardly say it this way. Though actually, if you took the word apart you would expect “in a frightful way,” and that older, more literal sense does still exist — but the everyday British use is simply very.

非常、極為（英式，偏老派或裝腔；跟「害怕」幾乎無關）