They provide a civ-wide bonus to your empire. If you like, you can sell that bonus (while keeping it yourself) in exchange for techs, money, etc, to the AIs, or buy it from them if they have the trade good.

If you lose the planet the trade good is on, then the conqueror will gain it's benefit and you lose it (same as with a wonder). Anyone you traded it to will still have the benefit, though, in this case.

One thing that should be noted is that they can't be resold to other players; you can purchase (or sell, if you own the trade good) the right to use the trade goods, but you can't sell that right to other players (unless you own the planet the trade good is on). So if I bought Gravity Accelerators from the Iconians, all of my ships would have +1 speed, but I couldn't then sell Gravity Accelerators to the Yor (unless I captured the Iconian's planet that housed the trade good).