In principle, "це" means "it" or "this" when it's a pronoun. "That" would be "то". However, in English it's very natural to say "That's a dog" e.g. simply pointing at a picture and saying it. In Ukrainian in that case we tend to say "Це собака". "То собака" (which would be the proper translation of "That is ...") is not really used as a standalone, more when some contrast is present ("Це ..., а то ..."), it sounds a bit unnatural.
So we decided to allow translating "Це ..." as "That's" and the other way around because A LOT of users opt for that, it's quite natural in English.
Right now the more natural order is set as default.
This weird one is accepted because from the technical point of view it's grammatically correct.
But please, to those of you translating the Ukrainian sentence too literally, word for word, this is not natural in English! Please use "Please, show me ..." or "Show me ..., please" instead.
Цей (m), ця (f) and це (n) all mean "this" in the sense of "this scarf" or "this car", as an "attribute" of a noun, to describe the noun (e.g. This scarf is mine)
Це also happens to play the role of "this" in the sense of "it", as in "This/It is ..." (e.g. This/It is my scarf).
It's similar to German where "das" means "that" for neutral nouns ("Das Buch ist meins"), but also means "this" in the sense of "this is", no matter what gender comes after ("Das ist mein Buch").