The cross-currency pairs or cross rates as they are also known, combine currencies of the major economies but do not involve the US Dollar. For example:

The Euro to the British pound -- EUR/GBP
The Euro to the Japanese yen -- EUR/JPY
The Pound Sterling to the Japanese Yen -- GBP/JPY
The Euro to the Swiss Franc -- EUR/CHF
The Australian Dollar to the Canadian Dollar -- AUD/CAD and the
Euro to the Canadian Dollar -- EUR/CAD, to name just a few.

As they do not include the US Dollar, they are less traded, with lighter volumes, and less liquid than the Majors. They are more volatile, offering good trading opportunities. At the same time, good risk management rules should be in place to cater to sudden price fluctuations and wide swings. The cost of trading the crosses is a bit higher than the Majors.