Forex pairs are divided into two broad categories. There are the majors that include the most frequently traded and most liquid currency pairs and the crosses. The majors all include the USD as either the base or quote currency. The cross currency pairs do not include the dollar because they "cross" two other currencies with each other.
The most actively traded currency pairs are the majors. These are all crossed with the USD and make up the majority of annual trading volume in the forex market. For example, according to the Bank for International Settlements the EUR/USD makes 27% of all forex trading alone. If you combined the trading volume of the EUR/USD with the GBP/USD and the USD/JPY you would have captured 52% of annual trading volume. Most traders start their forex career by becoming familiar with the most popular majors before beginning to trade the crosses or smaller major pairs.