If something is tinny, it sounds weak and a little metallic. Music played on an old-fashioned transistor radio would sound tinny compared to a fancy new stereo.
Tinny sounds are vaguely unpleasant, and tinny objects are poorly constructed, of cheap metal. You'll have more fun cooking in a heavy cast iron skillet than a thin, tinny pan. You could say that tinny things either sound like tin being struck with a spoon or appear to be made from tin. And if something tastes tinny, you can detect a metallic flavor in it.