Traveling vs. Travelling
There are many instances where words that are the same are spelled differently in different countries that use English as a primary language. American spellings of specific words do differ from the commonly acceptable forms in Britain. Traveling and travelling are an example of this phenomenon.
Traveling and travelling are both present participle forms of the word travel. This word means to journey.
1. Will you be traveling/travelling overseas this summer during your vacation?
2. My parents love traveling/travelling now that they are retired and have the time to do so.
3. I know that you would like to talk with my grandfather right now, but he is currently traveling/travelling.
4. Traveling/Travelling can get very expensive, but there are ways that you can save money if you need to travel on a budget.
5. Sarah and Mark are traveling/travelling to Jekyll Island, GA this summer to study the sea turtles and their nesting habits.
6. While my mother enjoys traveling/travelling, my father would prefer to stick close to home and tend to the plants in his garden.
The differences in spelling have to do with the preference for one versus the other in the US versus Britain. In Britain, travelling is the preferred spelling. In the United States, traveling is preferred. This preference can be traced to the early 20th century.
As with many cases in English, one spelling is no more correct than the other. However, you should always consider your audience and choose the spelling that is preferred depending on where and to whom you are writing.