Pairs trading is, as you might expect from the name, betting on two different financial products at the same time. The idea is that two underlying products are in some way related, so you eliminate some element of chance compared to simply making a single bet.
For instance, one form of pairs trading is to bet on different stocks from the same market sector. You look at their strength relative to the sector, and pick the best and the worst ones. You would buy the strong one, and sell the one with less relative strength. This works well in sectors such as commodities, oil and electricity.
See what you have now achieved. You have eliminated one variable in your betting. If the energy sector as a whole goes up or down, you don’t really mind. If the sector goes up, you expect that the one with greater strength will rise more than the weaker one. Similarly, if the sector goes down, you expect the weaker stock to go down more than the strong one. The overall state of the economy or of the market sector is not much of an issue, you are simply betting that you will come out on top by betting on the comparative merits of the two stocks.
Another way to pairs trade is to pick two related commodities, such as gold and silver, and look at how their relationship has progressed, and whether there is a current imbalance that can be exploited. You need to be mindful of whether a “correction” is likely soon, by looking at the technical analysis, but the principle is that the prices will move back in line with each other over time, and you bet appropriately. Again, what you have done is eliminate the unknown of whether the government will issue more money, or public confidence will change, devaluing the currency or in other words increasing the cost of precious metals; or the opposite, that gold and silver are not so prized because the economy is looking good.