The story
Myötähäpeä is Finnish for the embarrassment you feel on someone else's behalf. It is a compound of myötä, 'along with', and häpeä, 'shame': shame that travels along with another person's. Wiktionary dates the word to around 2004, which makes it young, and it is now in Kielitoimiston sanakirja, the standard dictionary of modern Finnish.
The feeling is older than the word. Other languages have their own compounds for it: German says Fremdscham, 'stranger-shame', and Spanish vergüenza ajena, 'someone else's shame'. English manages with phrases such as second-hand or vicarious embarrassment, and in speech with one syllable that started life as a verb: cringe.
What makes myötähäpeä hard to translate is its direction. Ordinary embarrassment is about you. Here you have done nothing wrong, yet your face goes hot and you look away from the screen, wanting the moment to end for someone who may not even notice it is happening.
A scene: a wedding reception in Tampere. The best man's speech was meant to last three minutes and is now in its twelfth. He has reached the story about the stag weekend that everyone begged him to leave out. Half the room studies the tablecloth, and the bride's grandmother pretends to look for something in her handbag. That shared stare at the linen is myötähäpeä.