How is difficulty of a sudoku puzzle determined?

Difficulty of a sudoku puzzle can be determined in various ways.

One simple way to determine difficulty that some people use is how many cells are given at the start of a puzzle. On average across a sample of puzzles this is a reasonable approximation to difficulty level, but is not in and of itself the most accurate way.

The best way is to determine two things.

First, the number of available logically forced moves at each stage of the puzzle (the degrees of freedom to solve). Thus if there are nine moves you can make at time t, the easier the puzzle relative to one where there is just one move, as you have to find that just one move that you can make.

Secondly, there is the 'sophistication' of the pattern you need to use. If just spotting that you have to use a number to meet a rule that is simple; if you are looking for more complicated patterns such as having 1,2 1,2 and 1,2,3 and realising the one with 1,2,3 must be 3 (all within the same row, a column or a 3 x 3) then this is a slightly more complicated pattern.

If you have to look for even more obscure patterns to solve again, then it is harder. And the more times you need to look for these patterns to solve a puzzle, the harder it is again.
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