A non-logical symbol is a thing or a word that doesn't have any rules that govern how it can be used in a logical argument. It's like a toy that you can play with in any way you like, but you can't use it to create a rule for the game.
For example, in a logical argument, the words "and," "or," "not," and "if…then" are logical symbols because they have rules that tell you how to use them in a logical argument. But a name, like "Emma," or a number, like "7," are non-logical symbols because they don't have any rules attached to them when used in logic.
Think of it like building with blocks. Logical symbols are like building blocks that snap together in very specific ways, while non-logical symbols are like "free-build" blocks that you can use to create a structure in any way you like, without needing to follow any specific rules of construction.