This is the style of travel long term, slow, when you take several months or years to make your way around the world, staying in each location for long enough to really soak up the culture.
Long term travelers are often budget backpackers, trying to make their travel fund stretch for as long as possible by staying in hostels and looking for cheap food and attractions.
Rather than other short term types of travel, long term travel often becomes more of a lifestyle choice.
Sometimes these types of travel experiences are funded by savings, or sometimes long term travel can be funded by working on the road.