VirtualPrivateNetwork. You buy a vpn service from a provider, and they act as a proxy to the web. You have encrypted traffic that goes to the vpn, which then gets forwarded to the destination(in this case, instagram). The reply comes from instagram to the vpn, and then goes to your machine. Anyone watching the traffic will see communication to the vpn, but won't see the final destination.
Some of the more totalitarian countries will block vpns, so it isn't universally foolproof, but for nominally (semi)open countries, it'll get past restrictions.