The act of staring implies a visual focus, where the subject of the gaze is objectified. The notion of staring also implicates the looker in constructing themselves as a subject. They might be wanting to make themselves notice.
They might also find you extremely attractive and unable to look away. (happens in most of the cases!)
If staring happens continuously, they want to check on your activities , knowing you better but from far.. normally guys do that when they really don't won't to spoil things with girls and want to know the girl beforehand so that they don't miss out a chance to amaze you!
But since Mister is smiling like crazy that means it's your face that he keeps looking at! He must be star-struck by you!
Staring someone, normally pressurises the one being stared to look back. It might just be another way to win your attention. Especially when you do stare back and they continue staring or smile lightly with their eyes. But he literally smiles AND IF HE'S GRINNING THEN HE'S INTO YOU!
Staring is also sometimes used as a technique of flirting with an object of affection. If dirty looks are plastered on their face then its that.
Since you also did smile back you looked more approachable and amiable.It also dissolves the barrier that you might otherwise have created and he mustered courage thankfully because of you and atleast came to talk to you!
He likes you if that's what you wanted to know! Now shine your smile and catch him (if you want :) )