A preposition is the small word that gives two things a relationship. Take it away and the sentence no longer tells you anything useful.
The cup the table.
The cup is on the table.
We meet noon.
We meet at noon.
Why we need one
Is only says that something exists. It does not say where it is, when it happens, or who it is for. The preposition does that job.
The cup is hot. → a fact about the cup.
The cup is on the table. → where it is.
We meet at noon. → when.
This coffee is for Rex. → who it is for.
The question it answers
Do not start by memorizing a list. Ask which question the word answers.
- Where? in the bag, on the table, at the door.
- When? in the morning, on Monday, at seven.
- Who, or what about? for Rex, with a spoon, about the menu.
The rest of this course is those questions, one cafe at a time.