Dimension is a broad mathematical term, that very loosely means "ingredient".

The numbers that you are used to 1,2,3,4 etc have one ingredient. That ingredient being "1". We call these "1 Dimensional". Such numbers are ussually useful, but sometimes they are not able to capture the reality of a situation.

You can count cookies with 1D numbers, but when you want to describe WHERE you are, you need three ingredients (UP, RIGHT and FORWARD). Hence we live in a "3D world".

You might use more complicated numbers to describe your situation in more detail. Perhaps you want to know where you are but also how hot it is, which would require 4 ingredients (4 dimensions).

Physicists generally are often interested in WHERE and WHEN, because they are specifically interested in movement. The physics of a situation that doesn't change does not require a professional after all. Hence, (for their purposes), 4 ingredients are needed to describe a situation.

Sometimes physicists will use 6 ingredients: 3 for where (position) and 3 for where will you be (velocity).

Sometimes they are interested in a situation where some ingredients don't matter. In simple harmonic motion, there is a simple repetition, so only one ingredient is needed to describe the where and another for when.

By changing which number systems are used for the mathematics, we can make calculations easier or clearer or link two problems that seem unrelated at first.

Sci fi have often (incorrectly) used the word dimension as a stand in for "universe" or "world". And this has led many snake oil salesman to making videos that claim the "fourth dimension" or "fifth dimension" to be some mystical hidden place.

Dimensions don't have an order so calling anything the 4th dimension is misleading in and of itself, never mind the weird pseudo science that the term is used to push.

Cake could be said to be 3 dimensional. Any basic cake is some combination of flour, egg and milk and so we could label each cake with a 3D number and discuss which 3D numbers correspond to nice cakes and which correspond to failed cakes. For example (0,0,1), or a cake containing only milk, would be a failed cake.

If I then came along and showed you a chocolate cake, suddenly I'm adding a "fourth ingredient": chocolate. But there's nothing mystical about chocolate and it's only "4th" in the sense that you weren't considering it beforehand and now you are.