to travel second class

Many types of transportation (trains and planes for example) have a "first class" section where people pay more for more luxurious accommodations and another section (commonly called "coach") where the prices are more affordable.

Most appreciated
Thanks a lot

You seem to be reading, at a guess, older British material. On British trains, there used to be three classes, first, second and third, with descending levels of comfort and space. Third class was finally and belatedly abolished in 1956, and in 1987 second class was renamed 'standard class'.

Yes you are right.
Thank you for your good explanations