Tours are a specific form of sport organisation. A team will travel a long distance - usually to another country, but for very local teams, perhaps just a long distance in their own country - and then stay there for many days, and play a series of matches, perhaps all against the same opponent, perhaps against many different opponents, before returning home.
They are common with international teams in rugby union and cricket, and most professional association football teams will have a pre-season tour where they travel to another country to play exhibition matches. The USA and the Far East (Singapore, Malaysia, Thailand, Japan, China, Taiwan in particular) are common places for pre-season tours to go.
There is a distinction between a tour and a tournament (such as the Football World Cup), but I'm having trouble expressing it clearly; perhaps someone will clarify that in the comments.
A cricket tour will involve the representative team of one country travelling to another, usually for two to four months, and playing a number of matches against various first-class (the highest level below international) teams as a warm-up, then playing a formal series of Test matches against the representative team of the country they are in. The "touring team" or "tourists" stay in the country they are playing against for the whole duration of the tour.
A typical example might be the Australian team travelling to England.