Backtracking is a stone's throw from the mathematical concept of permutations so it might be better to look up visualizations of that and work from there. This one seems good: https://pebreo.github.io/combinations-visualization/
The number of permutations of n items is n!, because at every position you can place one item from all the items that haven't already been placed. Backtracking basically recursively produces all n! solutions (where every recursion depth is one position) similar to DFS brute force enumeration with the only difference that it also continuously evaluates partial solutions and short-circuits if it detects a partial solution that is guaranteed to make any complete solution containing it invalid.
E.g. if you want to enumerate the permutations of 4 people standing in a row, there are 4!=24 ways to do it. However, if you add the condition that Alice can't stand next to Bob, you can short-circuit the enumeration early as soon as you detect that Alice and Bob have been placed together (such as Alice-Bob-?-?)
You could also have more complex scenarios where every position has its own disjoint set of items to choose from.
What you do with the enumeration is up to you. Maybe you just want to enumerate and display all possible permutations. Maybe you just want to produce the best or k best as determined by some fitness function.
Although the case they use is almost perversely simple. Imagine in a 'real' sudoku that each number might need to be backtracked multiple times, such that the algorithm is regularly going almost back to the start.
