One troy ounce is exactly 31.1034768 grams. It is a different and heavier unit than the ordinary ounce of 28.35 g, and the difference of about ten per cent is why precious metal prices are always quoted in troy ounces specifically.
About the units
The troy system takes its name from Troyes in France, a major medieval trade fair town, and it survived for precious metals and gemstones long after the avoirdupois system took over everything else. A troy ounce is 480 grains; an avoirdupois ounce is 437.5 grains. The two systems share the grain, which is why the comparison is exact. A troy pound is twelve troy ounces, 373.24 g, making it lighter than an avoirdupois pound despite its heavier ounces — a crossover that has caused confusion for centuries and is the reason gold is never priced by the pound. The troy pound itself is now essentially obsolete; only the troy ounce remains in active use.
The exact factor
The exact value is 31.1034768 g, defined as 480 grains where a grain is exactly 64.79891 mg. The ratio to the avoirdupois ounce is 480 ÷ 437.5 = 1.09714..., so a troy ounce is about 9.7 per cent heavier. Useful reference points: a kilogram is 32.1507 troy ounces, and a standard gold bullion bar of 400 troy ounces is 12.44 kg. A one-ounce gold coin such as a Krugerrand contains one troy ounce of gold and therefore weighs more than an ounce in ordinary terms.
Where you meet this conversion
Gold, silver, platinum and palladium are priced per troy ounce on every major exchange, so any conversion of a bullion price to a per-gram figure runs through this number. Jewellery, coin collecting and assay work use it throughout. The trap for a general reader is a news report giving a gold price "per ounce" without specifying troy — reading it as an avoirdupois ounce understates the mass by nearly ten per cent and therefore overstates the price per gram by the same amount.