The usage of ~ and & are specific to the network, and not supported on all networks. In regards to the networks that I have seen them used on, here's a little chart that you can use.
~ Founder
& SuperOP/Channel Admin
@ Channel Op
% Channel Half-Op/Help-Op
+ Voiced
That is in the normal order, from highest to lowest.
As to what it does, it just allows an additional level of control in the channel, higher than ops, but lower than founder.
