An iPhone is blacklisted when it is found in the global blacklist database of network carriers.
When an iPhone is blacklisted, it prevents anyone from activating the iPhone with any network carrier until it has been removed from the blacklist.
An iPhone reported as lost or stolen gets in the blacklist through its IMEI number.
Wireless network carriers are the ones responsible for putting an iPhone on the blacklist. The top two reasons why an iPhone gets blacklisted are:
(1) it was reported as lost or stolen, and
(2) the iPhone is acquired with outstanding and unpaid bills.
The best approach for removing the Blacklist status from your device is to contact the Original Owner or the Mobile Network that Blacklisted it. If you are not able to do that, there are some Unblacklist services, that can remove the LOST/STOLEN status from your iPhone, so you can start using it again.
Check this service out and see if your network is supported: iPhone Unblacklist Services