To genuflect is to bend one knee to the ground, usually as a sign of reverence or respect. It’s mostly associated with churches and religion, particularly Catholicism – people genuflect before entering a pew. It also has a metaphorical meaning: to show excessive deference or subservience to someone. As in, ‘I'm not going to genuflect to my dog just because he’s the most gorgeous boy in the world’ (even though I spend a lot of time cramped into weird positions because he’s asleep on me and I don’t want to upset him by getting blood back into my limbs).
‘Genuflect’ comes from a Late Latin word, genuflectere, and it’s pretty straightforward when you break it down: genu means ‘knee’ and flectere means ‘to bend’. So literally, knee-bending. The Romans were nothing if not literal. (Oh, and ‘Late Latin’ refers to the form of Latin used roughly from the 3rd to the 7th centuries AD i.e. when the Roman Empire was beginning that falling business. At this point, Latin was becoming less standardised, picking up influences from regional dialects and the languages of the various peoples who were interacting with (or invading) the Roman world. Grammar got simpler, new words were created and it moved away from the highly polished Classical Latin of Cicero and Caesar.)
Flectere has been quite busy in the English language, popping up in all sorts of places. For example, it’s where we get ‘reflect’ from (bending light), ‘deflect’ (as in turning aside) and ‘inflect’ (bending as in modulating something, usually your voice). Meanwhile, poor old genu has been rather left on the sidelines. Its only real claim to fame beyond genuflect is ‘geniculate’, a scientific term that means ‘bent abruptly at an angle like a bent knee’. Sounds painful.
You might look at ‘genuflect’ and think ‘well, surely that’s also related to “genius” and “genuine”’, unless, unlike me, you have a life. Well, I’m afraid that, despite the resemblance, those words come from an entirely different Latin verb, gignere, which means ‘to beget’. So no knees involved whatsoever. But, if you’re hungry for more knee-based etymology, the Latin genu is related to the Greek gonu (also meaning ‘knee’), which gave us gōnia meaning both ‘knee’ and ‘angle’. And that means that polygons, pentagons and hexagons are all essentially named after knees. You’re welcome.