According to three different dictionaries on the web, galoshes are shoelike things made of rubber or plastic, worn over ordinary shoes in rain or snow. I grew up using the word to refer to clumsy rubber rain boots worn by children, usually red but not always. They were worn over shoes, or over socks alone.
dictionary.com tells us that the word comes from the Middle English "galoche", a shoe with a wooden sole. They say that "galoche" is derived from Old French, but not how nor why. Webster 1913 discusses galoche at length: It is good!