I understand that in order for an object to maintain circular motion, its velocity vector must be travelling perpendicular to its position vector and constantly changing inwards, hence an acceleration towards the center of the circle. I know that the acceleration towards the center is typically caused by other forces, like tension on a string, and that these are called centripetal forces I believe? However, objects in circular motion tend to want to be away from the center instead of towards. A bucket of water tied to a string and twirled around in a circle will result in the water staying in the bucket: if the water is exhibiting circular motion, would it not thusly be accelerating inward, and thus escaping the bucket? I've heard that it's a difference of frame of reference, but even looking from out to in, I can't see how the water would be accelerating inward and yet remain in the bucket without support. Would there not be some force pushing the water into the bucket? And yet, centrifugal force is considered a fictitious force. I don't understand. I know I understand some level of physics but please explain it like I'm 5 because I can't seem to actually understand this.
Like you said, objects in a circular motion want to be away from the center of a circle instead of towards it. Centrifugal force is the term to describe that specifically. It's a "made up" force, because there is no force pushing an object away from the circle.
Q: How is there no force pushing an object away from the circle?
A: An object moving in a circular motion is at all times already trying to move away from the circle. If you take the bucket of water for example, and suddenly deleted the bucket, the water would keep flying in the straight line it was trying to go in. The direction it would fly would be sideways, perpendicular to a line drawn to the center of the circle and not outward away from the center.
Q: Is the water accelerating inward?
A: Yes! The bucket pushes the water keeping it from going in a straight line. Likewise, the string pulls the bucket which keeps the bucket from flying out. And you are spending the energy to cause the force that is being applied to the string. This is known as "centripetal force". It's the force that makes the circle going objects change direction.
Q: If there is force or acceleration inward, why doesn't the water fly towards the center?
A: Acceleration is not a change in speed. It is a change in velocity, which is a combination of speed AND/OR direction. So the water doesn't fly inward because centripetal force only causes a change in direction (the bottom of the bucket keeps the water from going straight). If someone punched the bottom of the bucket while it was swinging in a circle, then the water would fly inward out of the bucket because that would cause a change in speed toward the bucket.
Short summary: Nothing is pushing the water into the bucket, the bucket is pushing the water so it continues to accelerate in a circle. The water wants to go straight. That is inertia.