I just got off the phone with Honeywell. If you only have a 4-wire older system, you'll only be able to use the fan in the "auto" position. It won't let you use the fan-only selection. You need a 5th wire for power for the wi-fi side of the thermostat. Call Honeywell and they'll walk you through it for free.
The C wire, not to be confused with R or RC is the return path. Think of it as a ground, though technically not. Based on the information above, none of the wires O, B, W, G, R, Y, will work for C. So they can not be jumped over to the C connection. The C wire, usually the brown wire on the transformer, the low voltage (24v) is the common. However, no matter the color, there are only two low voltage wires on the transformer, one power (Red, Blk, Yel), one common. So what ever color not representing the power, is the common C. Of course, AC current flows both directions, but trying to make this simple. Anyway, that wire (the non power wire) needs to come in to the thermostat for the C connection. With an extra wire (any color on the wire loom at the thermostat can be traced back to the 24v transformer and connected to the common, usually color brown wire). That extra wire used, the new color will become the C wire. Just a note, one issue I have had with the WiFi thermostat is the fan ON and Auto don't work independently. So for example, if the thermostat is selected to run the fan ON - no cooling or heating, I've seen that not work. It can be fixed too, just not answering that.
Best Answer
Go ahead, hook that blue wire up to C and use it for your Ecobee
As the terminal strip on your furnace control board is typical in that it has room for 2 wires on each screw, you can simply land the blue wire on the furnace control board's C terminal alongside the white wire that's already there.
BTW: the brown cable you're asking about can simply be left alone -- it's the cable that connects your thermostat's yellow wire (Y terminal) and the furnace control board's C terminal to the compressor contactor in your air conditioner so the thermostat can turn it on and off when things get sweltering in the summertime.