Fremd is an adjective meaning, in this context, "alien" or "foreign." Schämen is a (reflexive) verb meaning "to be ashamed" or "to be embarrassed." In combination, they mean "to be ashamed for somebody else who is behaving in an embarrassing way." The verb is used, in particular, if there is some indication that the culprits themselves are not embarrassed, even though they should be. For example, one may conclude the description of the outrageous behavior of some spectators at an event with the sentence, "Ich hab mich fremdgeschämt (I felt embarrassed [for these people])."
The verb appears for the first time in the Duden, the official German spelling dictionary, in 2009. That is, it is of relatively recent coinage, and I was not aware of it until I saw it used some years ago in an online forum. Since then, it has become a favorite of mine for several reasons. For one, it succinctly represents a feeling that overcomes me at times. It also demonstrates, again, the ease with which one can combine seemingly unrelated words in German to capture, in a compact form, some nuanced meaning—apparently, this process is still going on in the German language community.
I am well aware that using our current Word of the Month as a foreign word in English is just about impossible. It is, first of all, a verb, and I have no idea how you would conjugate it in English. In addition, it is a reflexive verb, which makes this task even more challenging (see the example in the opening paragraph). I decided nevertheless to make fremdschämen a Word of the Month for the reasons stated above. People traveling to Germany or reading German papers may encounter it, and students of the German language may find it an interesting neologism in its own right.
6 hours ago