Ticket to Ride is a game produced by Franco-American publisher Days of Wonder. It is fairly quick and light, and often regarded as a “gateway game.”
In a game of Ticket to Ride, players are competing to gain the most points, which they do by claiming routes across a railway map.
At its most basic level, Ticket to Ride involves 3 elements, 1) collecting train cards of different colours, either face-up from a common pool, or blindly from a deck, 2) spending those train cards to place plastic trains on a map, thus claiming that route, (and gaining some points for it) and 3) picking up tickets, showing a pair of linked cities- players can take any 1 of these actions each turn, and the game continues until 1 player has exhausted their pile of plastic trains. At game end, players gain points for tickets in hand that they have completed (i.e. plastic trains of their colour form a continuous chain between those two cities) but lose points for incomplete tickets in hand.
The game was first issued with a Map of North America, but has since been expanded into varied locations with numerous twists.
The Board Game Geek page is a jumping off point for a seemingly endless number of variations on the game. This summary page is a helpful place to start
The official website of the Publisher, Days of Wonder is also worth a look