Ok. The fourth dimension can be defined as either time or another spacial dimension, which are two very different things. I'll start with time since it's a bit easier to visualize.

From our perspective, each dimension uses the dimension above it to move. For example, if a flatlander is living on a plane, and discovers a way to move to a higher or lower plane, it would remain 2D while moving through the third spacial dimension of up or down. When we move from one place to another, we do not need another spacial dimension, since only three exist in our universe. Instead, we use time. Even light takes eight minutes to reach Earth. Some people like to use the analogy of a recipe. We have three cups of space (length, width, height) and one cup of time (a single timeline). The fifth dimension after time is a plane made up of multiple timelines, or parallel universes. If you were a fourth dimensional being - a time traveler, technically - you could go back in time, change something, and end up in a neighboring universe where something is different, therefore traveling through the fifth dimension. Following the pattern, the sixth dimension is spacial time, or multiple time-planes. The difference between universes in our same plane and universes on higher or lower planes is unknown, but some people think that, given that the big bang is the start of time, all parallel universes begin with the big bang while those on different planes have different origins. If there was only one possible way for a universe to be created, then the sixth spacial time dimension would probably not exist.

Note: I'm using terms like 'the fifth/sixth dimension' as placeholders here. Some scientists define the word 'dimension' itself differently, and end up with ~10 dimensions in between these. However, it's unlikely that there are infinite time dimensions, because you would eventually reach a point in which all possible universes that can exist do, and then there's no point in continuing.

4d or 5d space is more commonly used in math. The best three-dimensional model of a fourth dimensional object I can think of is the Klein bottle (two Mobius strips sewn together). In the fourth dimension, the intersection would not exist. Most videos you've watched probably involve rotating shapes, since without the movement it would look like a normal three dimensional object. I've personally never been able to truly visualize a 4d object, although a lot of videos claim you can.

That's the best way I can describe the basics of it, anyway. Every time I research it, I learn something new that changes my entire perception of how the world works.