The purpose of using a fulfillment handler (the functions passed to then in your example) is to wait for the promise to be fulfilled and then, at that point, do something else.
The goal of that code (apparently) is to wait until the cleanRoom promise is fulfilled, then start the removeGarbage process, and then when that is fulfilled, start the winIcecream process. It's also worth noting that if cleanRoom's promise was rejected instead of being fulfilled, removeGarbage wouldn't happen at all, because it's in a fulfillment handler, not a rejection handler.
If you did this instead:
cleanRoom().then(function() { /*...*/ });
removeGarbage().then(function() { /*...*/ });
winIcecream().then(function() { /*...*/ });
...all three processes would be started immediately and run in parallel (to the extent whatever async process they're modelling can run in parallel with other JavaScript code). There'd be no coordination between them at all.
...how is it happening that the winIcecream() will run after resolving the removeGarbage promise...
then, catch, and finally create and return new promises. Those promises are fulfilled or rejected based on what happens to the promise they were called on and what happens in or is returned by their handler. So for example:
doThis()
.then(function() { return doThat(); })
.then(function() { console.log("done"); });
Let's call the promise from doThis() "Promise A". Calling then on it creates a new promise ("Promise B"), that will either be rejected (if Promise A is rejected) or will call its handler if Promise A is fulfilled. Promise B is resolved to whatever that handler returns. In the code above, suppose Promise A is fulfilled and doThat() returns a promise ("Promise C"). Now, Promise B is resolved to Promise C — whatever happens to Promise C is what will happen to Promise B. If Promise C is fulfilled, Promise B is fulfilled, and the second handler with the console.log is called.
The MDN article on using promises may be helpful.