A prerequisite to understanding is knowing the CTE syntax ("WITH"). That's just a group of SQL queries that can refer to one another. It's extremely useful for making modular SQL queries and has nothing to do with recursion.

Then when you use "WITH RECURSIVE", the queries can now refer back to themselves. This is just a for loop over a queue of SQL results, conceptually. The part before the UNION ALL fills the queue to start, and the part after the UNION ALL runs once for each result in the queue, adding all results back into the queue.

If you understand this, then you can understand the Sudoku or Mandelbrot examples (definitely don't start with trying to understand these two though). For example, the Sudoku example contains one recursive query, "x(s, ind)". As explained on the page, "s" is the puzzle (unsolved spaces shown as ".") and "ind" is the index of the first unsolved space (or 0 for a solved puzzle). It creates an unsolved puzzle in the initial setup. The for loop body finds all valid values for the first unsolved space, and the next index to solve; then puts all these results into the queue. The final (non-recursive) SELECT in the CTE looks over all results in the queue, and returns the one where the index is 0 (the solved puzzles).