I went on a five week trip to Europe in September/October 2016. I did not check a bag, but instead brought a backpack, a purse, and carried an extra jacket. I traveled on six airplanes and visited three countries during this trip and learned a bit about what it means to travel light.
How to do it
This style of packing requires some amount of forethought. I recommend looking at the weather for each of the places you are going. Make sure you pick clothing that can be worn in different weather conditions by choosing clothes that are thin and can be worn in layers. Look at your itinerary and decide when you will be able to do laundry. I was lucky enough to stay primarily with family and in Airbnbs, so I had a few opportunities to do laundry. Some hostels also offer laundry facilities and coin laundromats will be available in most major cities.
Although I knew that I would have plenty of opportunities to do laundry, I still packed about two weeks worth of clothes. I did this by packing two pairs of jeans and wearing one pair on the plane. I also packed about 13 pairs of socks and underwear and a mix of thin long and short sleeve tops. I wore a sturdy pair of walking shoes on the plane and packed a thin pair of sandal-type shoes. I carried a thick jacket on the plane and packed two thin jackets. I packed minimal toiletries with the plan of buying small amounts in Europe if I needed them. I don't wear makeup or bother with my hair, so I was easily able to save space by forgoing any beauty products and instead packing a beanie and a few hair ties for any bad hair days that might occur. My purse contained an iPad, phone charger, a few small pocket guides, money, and travel documents.
The advantages of packing light is great, especially if you'll be bouncing from place to place. I didn't need to worry about checking bags or lugging a suitcase around London or Paris. It makes travelling on public transportation much easier. I was also not tempted to buy too many souvenirs as I didn't have the space to pack it back home. Backpacks, in my opinion, are much easier to transport than suitcases. You have your hands free and don't need to worry about narrow sidewalks, walking down many stairs at a tube station, or climbing to the sixth floor at your Paris Airbnb. Without checking a bag, you don't need to arrive to your flight as early and you can get to your next destination as soon as you pass through customs instead of waiting for your checked bag as well.
Despite all the positives, traveling light did have some disadvantages. My shoulders started to suffer. My pack was good at alleviating shoulder stress because of the chest and hip straps, but my purse was another story. It sat on one shoulder and, after I was given a cast of a bear print in Slovenia, began to weigh down heavily. It made walking between accommodations a little more difficult than I had expected. Although I'm not someone who needs to wear a new outfit each day, I did get a little bored of wearing the same top every few days. After experiencing a much warmer time in Slovenia than I had planned, I wished that I had packed a pair of shorts, but didn't have the room to buy some in Ljubljana and pack them with me for the rest of my trip. I also was unable to bring my DSLR camera, something that I did wish I had brought at times.
I also found out, quite close to my departure date, that those cheap airlines that lure you in with $100 round trips do not allow you to bring on board anything other than a small personal item. You can get around this by upgrading and paying another $30 or $40 to bring on a larger carry on item. This makes the cheap airfare seem not so cheap after all. It's still better than paying to check a bag, and some airlines include priority boarding with your upgrade. When traveling light, always check the airfare bag allowance before heading to the airport!
Overall, I enjoyed traveling light. I'm glad I didn't have to lug around a suitcase wherever I went. During my last few days in London, I bought a medium sized suitcase that I did check on my flight back to California. This allowed me to only bring a few items onto the plane with me, while also allowing me to purchase lots of Buttons, Milky Bar, and Magic Stars. Despite caving and buying a suitcase in England, I had a hard time navigating from Hyde Park to Gatwick airport on the tube and a train with a suitcase. Both the tube and train stations were crowded, and lifting a suitcase up stairs with many Londoners rushing around was not my fondest memory of my trip. Although it allowed me to bring more things back with me, I don't believe it was entirely necessary.
Traveling light is doable, as long as you are realistic about what you'll need and use abroad. Oh, and having a great backpack will also help.