Data roaming occurs whenever your phone disconnects from your carrier's network and hops on another network. Roaming allows you to make calls, send texts, and use wireless data even when you're outside of your network's boundaries. The downside, of course, is that roaming data usually comes with extra charges to your account.
For example, let's say you take a trip across the pond to London. You get off the plane, and like magic, you have signal bars to call a Lyft driver to pick you up from old Heathrow airport. This happens because your wireless carrier has an agreement in place with a network in England to provide you with roaming service. If you have the roaming feature turned on, all of this will happen automatically.