Why is it so important / impactful to kill enemy villagers?

Pretty much title. I'm very new at this game, so please excuse my noob question. I noticed when watching casts of pro player games, that villager kills get highlighted way more than dead military units, even though villagers are pretty cheap and 3 dead villagers on a woodline with 15 villagers doesn't really seem that important (especially compared to half an army dying).

Thanks in advance!