The mint ratio simply defined as the gold/silver ratio, is an indication of how many ounces of silver are equal in price value to one ounce of gold. In other words, how many ounces of silver would it take to buy one ounce of gold.
Throughout history, governments have artificially set the gold/silver ratio for purposes of stabilizing the value of their gold and silver currency. In essence the mint ratio has been a government-established rate of exchange between gold and silver.
Only when a nation establishes an official exchange rate, the market ratio is normally very close to the mint ratio in that nation because of the potential for arbitrage. For example, if Switzerland uses a 17:1 mint ratio and the UK has a 14:1 mint ratio, an investor can trade her gold for silver coins in the UK and trade her silver for gold coins in Switzerland, although he has to take the risk of transporting the precious metals safely.
This bimetallist monetary system has been for instance practiced by the US government roughly from 1790 to 1870, which set by law the value of a unit of currency at a specific weight of a specific purity of metal. Of course, in doing so government is interfering with the workings of the free market and I do not expect that governments will revert to this outdated system anytime soon.
I personally wouldn’t use the relationship between silver and gold prices to determine whether the price for one of these metals is likely to increase or not. But knowing its definition could be useful for your financial literacy.