It just appears to show virtually the same action over and over again. Doesn't it?

It's much better to try to explain an algorithm in a few simple lines. Now the idea is to move the largest disk from the start position to the end position. For that, you have to first move the smaller stack of disks on top of it (1 disk less), as a Tower of Hanoi, to the help (extra) position; and afterwards, in the same way, move it back on top of the larger disk, now in the end position. So to move a 4 disk Tower of Hanoi from A to B, you have to move a 3 disk ToH from A to C, move the bottom disk from A to B, and move the 3 disk ToH from C to B, on top of the big disk.

(I happen to have explained how to solve a (physical) Tower Of Hanoi puzzle to my 7 year old son, only last week. Now that's a coincidence. The way I did it is start with 1 disk, next with 2, then 3; and every time he solved it, add one more disk to the puzzle.)