Public Bath
Give a coin and get hot water. So you hand over a coin and then you get hot water in the form of a bath. It's a bath for anyone willing to pay, making it a public bath.
せんとう
This is a jukugo word that uses the on'yomi readings of the kanji. You don't know the on'yomi reading of 湯, though, so just think about how when you get in the public bath, you're in Tokyo (とう), because there are a lot of public baths in Japan, and Tokyo is the most well known city there.
祖父の一日は、銭湯から始まります。
My grandfather starts his day by going to a public bath.