A grammatically correct sentence will, in almost all cases, contain a subject and a predicate. You use them carelessly because they are not complicated at all. At least functionally.
Schoolhouse Rock. Come on, you have nostalgia, too.
What the video explains in a suave, pleasurable voice is that a sentence consists of two basic parts: the subject and the predicate. The subject is the part of the subject that does something or is a certain way. The predicate explains what the subject does or is like.
It can get more complicated than that- but why should it?
For fun, why not look over this blog post and divide each sentence into subject and predicate? If you’re unable to, the sentence is ungrammatical! Look out for combined sentences and sentences with more than one subject.
The Wikipedia page for the predicate explains why the predicate can be a tricky and controversial piece of grammar.
GrammarMonster diagrams a few simple sentences so you can really get the idea.