Example sentences
tā他xǐ喜huan欢lǚ旅yóu游。
He likes traveling.
qù去zhōng中guó国lǚ旅yóu游。
Travel to China.
About this word
旅 means "journey" and 游 means "to roam, to wander", so 旅游 is travel for pleasure, going somewhere to look around. Its near twin 旅行 also means travel and is the broader, more neutral word, while 旅游 leans toward tourism and sightseeing and is what tour groups advertise. Both take no object: you 去中国旅游, never 旅游中国. Use 旅行 for the plain act of covering distance, and 旅游 for a holiday spent seeing places.
The story behind the character
旅
旅 is a flag on a pole with people trailing behind it. That is an army on the march, and in the old Zhou system a 旅 was a unit of five hundred soldiers. Xu Shen wrote 旅，軍之五百人爲旅. Only later did it mean traveling, which is why your 旅游 looks like a marching column.
游
游 is 氵 (water) with 斿 on the right, which gives the sound and once pictured banner streamers fluttering in wind. Xu Shen described the family as 旌旗之流, the streamers of a banner. Flowing, drifting, going without a fixed aim. Swimming and wandering are one verb in Chinese, and the character shows why.