Expeditionary warfare means that instead of fighting a battle or a war in your own country, you go somewhere else to fight. It's like when you visit your friend's house to play, but instead of playing, you have a big fight against your friend's enemies.
The military does this when they want to help another country that is having a problem, like a war, a natural disaster, or a terrorist attack. They send soldiers, ships, planes, and weapons to the other country to fight and protect it.
When they get there, they have to set up a base, like a camping tent, where they can stay and do all the things they need to do to fight. The soldiers have to be very careful because they don't know the language or the customs of the other country.
Expeditionary warfare is very hard because soldiers have to travel long distances, leave their families, and risk their lives. But they do it to help people in need and protect their own country from bad guys.