A "travel team" is an elite, competitive youth sports
Your local Little League or similar youth sports organization is probably made up of several teams who fill their ranks with children from a few towns, maybe a single county at the extreme, an scope narrow enough that you could drive to any of the ballfields it plays on in not much time. In contrast, a single travel team will usually draw from about the same area as one or more of these leagues, and so a season's worth of away games represents quite a bit of travel, thus the name.
Geographic breadth aside, the thing that most sets travel teams apart is their selectivity. While most local youth leagues will accept any child who shows up and pays registration fees, travel teams usually require aspiring members to prove themselves, either by admitting athletes on the basis of competitive tryouts or by recruiting "stars" from open leagues. In turn, good travel team players can expect to eventually move up to teams from even more elite leagues, creating a hierarchy that can extend from county to regional to state to, in some sports, national or Olympic teams.
Some travel teams operate during summer or the "off" season for their sport, so as to allow players to participate in local or school sports as well. Others embrace the opposite philosophy and operate on a year-round schedule, demanding that their athletes put team participation before all else - other sports, other leagues, or non-sport activity in general. The further up the "ladder" a team is, the more likely it is to take the latter approach.
In this way, travel teams can often compete with established school teams for athletes and attention, especially in sports like soccer or baseball that enjoy a dedicated following but not the widespread public admiration bestowed upon more celebrated scholastic sidelines like basketball and football. First-tier travel teams often compete in leagues equal in geographic breadth, and equal or better in terms of level of play, to large high school conferences. However, while students don't usually enter high school until age fourteen or fifteen, some travel teams recruit young athletes as early as age seven or eight. Increasingly, travel teams are seen as superior and preferable to school teams, offering young athletes both a more challenging sporting experience and better exposure to college scouts.