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Based on the [source code](https://github.com/sympy/sympy/blob/4c9630723d6d76a356ff6e4cc65e994783c54bd1/sympy/polys/polytools.py#L2337) which delegates to [this implementation](https://github.com/sympy/sympy/blob/4c9630723d6d76a356ff6e4cc65e994783c54bd1/sympy/polys/polyclasses.py#L601) among others, `base.diff((x, n))` means to compute the `n`-th derivative of `base` with respect to `x`. Any arguments to `diff` which aren't tuples get tupled with 1, e.g. `base.diff(x)` is more or less equivalent to `base.diff((x, 1))`. Multiple arguments essentially correspond to repeated differentiation, e.g. `base.diff((x, m), (y, n))` is more or less the same as `base.diff((x, m).diff((y, n))`.

Numeric arguments are indexes into the array of generators provided when the polynomial was created. That is, if `base` is defined by `Poly(..., x, y)`, then `base.diff((0, n))` and `base.diff((x, n))` are more or less the same. Similarly, `base.diff((1, n))` and `base.diff((y, n))`. This is handled by the method [_gen_to_level](https://github.com/sympy/sympy/blob/4c9630723d6d76a356ff6e4cc65e994783c54bd1/sympy/polys/polytools.py#L1810). That method also allows negative numbers to index backwards into the array of generators, i.e. `base.diff((-1, n))` is also equivalent to `base.diff((y, n))`.

The example from the other answer of `base.diff(y, 2)` gets interpreted as `base.diff((y, 1), (2, 1))`, however, since there is only 2 generators (`x` and `y`), this should lead to an exception being thrown in `_gen_to_level` as 2 is not a valid index into the array of generators.

That said, the example in the documentation is rather cryptic, and it is a bit bizarre to have `base.diff((0,0))` which would mean "take the 0-th derivative of the first generator" which is well-defined but corresponds to doing nothing.