It is basically an agreement between 2 parties to interest payments and principal on loans denominated in two different currencies. For example A borrows X amount of USD from B and in exchange, A lends X amount of Euro to B, within certain period of time.

The reason companies use cross-currency swaps is to take advantage of comparative advantages. For example, if a U.S. company is looking to acquire some yen, and a Japanese company is looking to acquire U.S. dollars, these two companies could perform a swap. The Japanese company likely has better access to Japanese debt markets and could get more favorable terms on a yen loan than if the U.S. company went in directly to the Japanese debt market itself, and vice versa in the U.S. for the Japanese company.