The word travel has more than one syllable—it’s a multisyllabic word. In American English, when a multisyllabic word ends in a vowel and a consonant (in that order), you double the consonant when adding a suffix only if the stress falls on the final syllable. For instance, in the word repel, the stress falls on the final syllable, which means that you double the consonant when you add a suffix: repelling. But in travel, the stress falls on the first syllable, so there’s no doubling.
“Traveling” and “travelling” shared the same fate as many other words in the English language that have two different spellings. The person who’s usually credited (or blamed) for this is Noah Webster—the Webster of Merriam-Webster dictionary fame. He was a linguist and lexicographer who greatly influenced American English. Webster preferred the shorter versions of many words that had multiple spellings. He included the shorter versions in his dictionaries, and, over time, they became dominant in the United States. At the same time, the rest of the English-speaking world gravitated toward the longer spellings. So, while both Americans and Brits can travel, the former can enjoy traveling while the latter can enjoy travelling.
The United States is pretty much alone in using the shorter form. Canada and Australia generally follow the rules of British English, and that’s why Canadians and Australians can be fond of travelling, not traveling.
By now, you probably know when to use which spelling—it should conform to the place your audience is. If you’re writing a paper for a college class in the United States, you should use the shorter spelling. However, if you live in the United States but are applying for a job in Australia, you could instead choose to use the spelling they prefer.
Travelling and Traveling: Examples
As a visitor traveling from the United States, you must obtain a visa, which you can apply for before you leave for Cuba.—Conde Nast Traveler
As the reporters who traveled to the Group of 20 summit meeting with President Obama from Hawaii piled out and walked under the wing to record his arrival… —The New York Times
Passengers travelling to Bristol Airport are being urged to leave extra time as roadworks clog up a major link road for an entire month. —Bristol Post
Originally from Athens, and having lived in London for five years, he’d travelled on the train specifically to head in to town to “see the drunken crowds. It should be fun.” —The Guardian