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If you're Jewishly observant, you are liable to be called a frummer. In Britain in particular, you may be called a meshuganner frummer.
In America, frummie means sanctimoniously frum. Frumkeit is the way of life of the frum, and Frumster is a dating website for the frum which boasts hundreds of successful matches.
I haven't been able to trace when frum entered the Jewish lexicon, but it does not appear to have been before the Enlightenment at the end of the 18th century. My theory is that it only became necessary to coin a colloquial expression for a religious Jew when significant numbers of Jews became frei (the opposite of frum, denoting those who had made themselves "free" from the responsibilities of Jewish observance).
Frum is Yiddish from the German, froom, meaning "religious" or "pious." Interestingly, froom also means "steady," when used of a horse. This may not seem to be a very flattering word to apply to Torah-observant Jews.
However, the underlying idea seems to be that steadiness and reliability - underrated virtues today - are essential in those who would commit themselves to a frum way of life. This jibes with our notion of emunah as faithfulness; that Jewish belief and practice are best conceived of as ongoing faithfulness to a relationship and a covenant.