What is Byzantine Agreement?

This was mentioned in a different question. However Wikipedia states it is proven to be unsolvable.

So I would like to know what it is in this context and - since it is unsolvable - what the protocols trying to achieve it are actually doing.

The problem is proven unsolvable if the number $t$ of faulty machines of total $n$ machines have a ratio $t \geq \frac{n}{3}$. So for $t < \frac{n}{3}$ it can be solved. Or it can be solved if the result does not have to be certain agreement but allows some uncertainty (which should be small), which might allow a higher threshold.