«Взуття» is the most generic term, akin to English 'footwear'. It can refer to any kind of shoes, any kind of boots or even slippers. Just, anything worn on your feet. It's an uncountable neuter noun. We don't usually use it in the shop (so «це взуття» is not something we'd say), but we can use it when talking about footwear in general (e.g. «я люблю́ купува́ти взуття́» 'I like shopping for footwear').

«Ту́флі» is a kind of «взуття́», «Туфлі» are normally not higher than ankles, and are usually made of leather or imitation leather, and usually have heels (however, on male ту́флі the heel is very low). Male and female ту́флі look very different:

«Черевики» are usually higher than «ту́флі» (but not too high, that would be чо́боти 'boots'):

There's some overlap in the meaning with «туфлі», especially when used with a diminutive suffix: «череви́чки». «Череви́чки» 'small череви́ки' is often used to mean «ту́флі», especially female «ту́флі». For example, Dorothy in the Ukrainian translation of the Wizard of Oz takes the Evil Witch's «череви́чки» (although calling them «ту́флі» also works).

Hope that helps!