I recently went on ebay and ordered this wifi signal booster.
It claims to boost it up to 300mbps.
My current signal is 105mbps.
Does that mean it will amplify it? Or will it just boost it from the signal it gets?
A "wireless repeater" or "range extender" connects to an existing WiFi network as a client and then extends this network by allowing other clients to connect to itself.
It is hard to say if it will allow your computer to achieve higher throughput as it depends on a lot of different factors.
You will find a fairly complete description of the device, including the manufacturer's data-sheet, at http://www.shop.bt.com/products/tp-link-tl-wa854re-300mbps-universal-wifi-range-extender-9L10.html.
The phrase "up to 300 Mbps" does NOT mean that it will convert a slower network to this speed; rather, it means that it will boost networks running at speeds up to this level.
It will amplify, in the sense that a weak signal will be rebroadcast at a level similar to that from the router, but this will not improve the throughput in its vicinity beyond what can be achieved with the received signal, even though you can talk to the booster at 300 Mbps.
So, putting the booster next to your device will give no improvement, nor will putting it next to the router.
However, by judicious placement the booster may be able to achieve, say, 200 Mbps with the router, while your laptop/tablet can communicate with the booster at the same speed, thereby doubling your throughput. This of course assumes that all your other wireless components have 300 Mbps capability.
I hope this somewhat simplistic overview helps.