This is one of my favorite topics to study. I think the Block chain does not in itself eradicate poverty, but creates a healthy and clean environment for honest human beings to enter the field and achieve social justice around the world. But we must not forget that just as bitcoin can eradicate poverty, it can cause chaos in the world if left unchecked, so governments better deal with it peacefully and avoid fighting the Block chain revolution.
This is kind of a vague question- the blockchain cannot eradicate and erase poverty.
Imagine a public ledger that is visible to the public that everyone can see all of the transactions happening in the world. If a person attempts to change the transaction in the ledger (for purposes of cheating, etc.), it will be invalidated by all the people checking the transaction history (miners). This in itself cannot eradicate poverty but it creates a platform where transparency is shown.
While this may have an effect in future transactions, it is still too early for its adaption wide scale.