English question, please help?

"Means". You're talking about the word "children" or "lollies", which is a single thing. You aren't talking about the actual objects. Putting quotation marks around the words would make it clearer: "Children" means "kids".

Children means kids. = the word "children"
Lollies mean sweets. = the objects

Means, i think. Mean sounds as if children is singular.

Strange but I think it's mean- both times. Strange that grammar check doesn't catch it. "That's what it means". That sentence makes sense to me, but not the other two. I think mean is already plural in your sentences without the "s". I COULD be so very wrong. Find an English teacher.