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The 0 (single zero) and the 00 (double zero) are the green slots on the roulette wheel. These pockets could receive a 35:1 payout if hit straight up. If there's a split, the payout could be 17:1. This type of bet is somewhat risky, but the payouts could be worth it.
As a general rule, 0 or 00 (the latter being mostly on American wheels but not elsewhere) will pay 35:1 odds just as any other single number bet. Of course, the zero(s) are the key to the house having an edge that guarantees that they make money in the long term.