Okay, imagine you're drawing a line. You know how when you draw a line, it's all connected and smooth, right? Now imagine that line is made up of different parts that aren't connected smoothly. That's what we call a discontinuity in linguistics.
So, let's say you're reading a story and you come across a sentence where the words don't seem to fit together smoothly. Maybe it's like this: "I walking the dog yesterday." That sounds strange, right? It's a discontinuity because the words "I walking" don't go together smoothly. It should be "I was walking."
Discontinuities can also happen with sounds. Like if you're saying a word and you pause in the middle of it, that's a discontinuity in the sound of the word. Or if you're speaking and you suddenly switch to a different language, that's a discontinuity because the listener wasn't expecting it.
So, a discontinuity is just something that breaks the smooth flow of language, either in the way words fit together or in the way sounds are produced. It makes the listener or reader stop and wonder what's going on.