Ok kiddo, imagine you're talking to your friend and you want to say "I am going to the store." In some languages, like English, you always have to say the subject of the sentence ("I"), while in other languages, like Italian or Spanish, it's not always necessary to say the subject. In these languages, when you leave out the subject, it's called a null subject language.
See, when we say "I am going to the store," the word "I" is telling us who is going to the store. But in Italian or Spanish, you could just say "vado al negozio" or "voy a la tienda" without saying "Io" ("I"). That's because the verb "am" or "vado" already tells us the subject - it's "I" or "Io" by default.
So, in a nutshell, a null-subject language just means that people don't always have to say the subject of a sentence because the verb already tells us who or what is doing the action.