Many languages have a single word or phrase to add for politely asking someone to do a favor or even do something they should do without thinking. This phrase is also used in offering something to another, like, "please help yourself" or "please have this seat." In English, it is "please"; in German, "bitte"; in Swedish, "var så god"; in Italian, "prego", and in French, "s'il vous plait". In German, Swedish, and Italian, this phrase is also used for "you're welcome." In English, we may also say, "be so kind to..." or "if you please" or similar, but they are infrequent in daily discourse.
Japanese, to my untrained mind, has at least three common ways of saying "please". I first learned "kudasai" as being the equivalent of "please". However, if you are asking for a service, you might say, "onegai shimasu" (the "u" silent). Then I noticed that "dozo" was used for offering a service. For example, as a server put a plate in front of you, he or she would say, "dozo" (please have this).
Then I started recognizing ください (kudasai) on signs. It was more or less like "Please don't litter" or "please stay back from train doors". That is, it is an instructional "please."
I found myself using "dozo" when I made way for someone else. For example, we set the train seats on the three across side to face each other as we were five adults. For more leg room, I moved across the aisle to an empty two-across seat. At a station, a couple got on and couldn't find an unoccupied two-across or even three-across seat, and so they sat in a three-across with a stranger. I got up, gestured toward the seats, and said, "Dozo." They gratefully accepted the seats and said "Thank you".
Sometimes, "Dozo" is said only with a gesture. For example, a flagman at a construction site would wave us on with a sweep of his hand towards his back.
This is by no means a paean on the politeness of Japanese society. It is a mixture of rudeness, unfeeling, ordinary politeness, and out-of-the-way politeness. Traffic is the perfect example of rudeness, and some women carry flashing buttons to warn gropers on the subway that they have been noticed. Like in many countries, the elevator protocol is to avoid eye contact. I've written about ordinary politeness above. We've had strangers go out of their way to find us station lockers.