The Silver Badge is an item that demonstrates we're advanced members of the Tamer's Guild who have already performed heroic acts. Amelie gives it to us when we go to the Guild's Tower after completing the Tyrant Mulcimer quest.
Only silver tamers and above can use warpstones, even though the player is a special case as Edward granted them access before being promoted. Besides this, being a silver tamer is a requirement to be allowed into the Drake Isles village, as they only let in strong tamers. More NPCs in the game will recognize us, so we will be able to enter houses or fight tamers that weren't available before.