Post-grunge emerged after grunge in the early 1990s following the newfound mainstream appeal of alternative rock. Generally, bands labeled as such are rock bands influenced by grunge. Their music often uses the distorted guitar, angst-filled lyrics and "loud-quiet" dynamics of grunge, albeit in a radio-friendly and commercial way. They arguably have more in common with 80's rock and power ballads musically.
While there are exceptions, many post-grunge groups do not explicitly refer to grunge bands as influences. Read more on Last.fm.