A sponsored walk is usually organised by a charity as a fund-raising exercise. They invite everyone to register with them and commit to walk the course e.g. 20km, or from one end of the country to the other. Each walker asks their friends and relatives to sponsor them, for example, either x pence / pounds per mile or a lump sum for completion of the whole distance. After the walk, the walker collects the money from their sponsors, in line with their pledges, and gives the money to the charity.

Typically, anyone can participate but there is a formal signup and registration process, and there is often a small fee. The point of the walk is to raise money for a charity, so there are quite specific rules and the charity makes sure it gets its money. For example, to participate you may need to promise to raise at least $X--and they may want your credit card number so they can be sure they get the $X. It used to be common for walkers to walk as far as possible, and donor to promise to pay so many dollars per mile. For health and safety reasons, and because donors prefer to know in advance just how much they are donating, "dollars per mile" is much less common. It is a lot more fun than just giving money directly. The walker gets to participate in a group activity and get healthy exercise. Donors feel that the walker is "earning" their donation and therefore "deserves" it. And it's a lot harder to turn down a friend who says "sponsor me" than to turn down a charity that says "donate to us."

In my experience, anyone could participate. Participants seek sponsors among friends and relatives, and the sponsors agree to donate an amount based on the distance walked by the participant. The event might occur just about anywhere, like a park or a cityscape that has been closed off on a weekend period of time. The event would be organized by or for some charity.