A trading pair is a function whereby you have two different currencies that can be traded between one another.
When buying and selling a cryptocurrency, it is often swapped with local currency. For example, If you're looking to buy or sell Bitcoin with U.S. Dollar, the trading pair would be BTC to USD. Similarly, it can be swapped with other cryptocurrencies in the same way. So when Bitcoin is being traded with Ethereum, the trading pair would be BTC to ETH.
Currencies can have many trading pairs with each other, for example Litecoin/Bitcoin (LTC/BTC) or Bitcoin/British Pound (BTC/GBP).