Yes, you need a C wire to power the Nest. However, you won't know if the brown wire actually is a C wire without either going to look at where it is connected at the furnace, or testing it with a voltmeter.
It's pretty simple stuff, but pretty hard to describe the possibilities since we don't know exactly how the installer may have wired it. The simplest might be to attach some pictures of how the thermostat wires are connected inside your furnace.
Orange or Brown are often used to control the direction of a heat pump. In your case, it seems like the installer chose the Blue wire.
Blue or Black are often used for the (C)ommon wire. Perhaps the installer felt Brown was closer to Black so used that? And Blue meant Cool... maybe...
There should be a wiring block that the thermostat wires are all connected to inside the heat pump (you will probably have to remove a cover). The wiring block will have similar letter codes.
