Why do people working at the airport need to know what the purpose of the tourists' trips are? [closed]

The vast majority of people at the airport do not need to know. A small number (1 to 3, typically) do. These people work in Immigration, deciding whether to let you in or not, or in Customs, deciding how thoroughly to search your possessions as part of deciding whether to let them in or not, or in a joint Customs and Immigration role deciding both things. That's who the "travel slip" is for. Most travelers only meet one person for this decision process, but a small number are sent to talk to more people for a final decision.

Some other people at the airport may ask to see your form, mostly to make sure that you have filled it out before you get to the front of the line where the people need to see it. In addition, some other people may ask you, typically before you get on the plane, to show your passport and (if needed) a visa. These people work for the airline and want to be sure they don't transport someone who won't be let in, since they might incur costs as a result of that mistake. Since many countries offer different tourist and business visas, these people may ask you about the purpose of your trip too.

There are various reasons.

Airlines and travel booking companies ask it, for segmentation (different price for different people), marketing purposes, and also to help "their algorithm" to better predict passengers travelling (and better estimate the "overbooking").

Custom, police, immigration. It is just a question, it helps to see how people behave and also to select next question. Easy question are easy discriminant (and get a first feeling).

immigration, airlines: also to check if your visa is valid. Airlines get often (depending on the country) a fine if transport you with a non-valid visa.

Other passengers and personal (e.g. restaurant, shops): just to be nice and start conversion.