I own a security company and we install cameras, access control, etc.
POE is Power over Ethernet.
A CAT5/6 cable has 8 wires or 4 pair. Orange, green, blue and brown and orange/white, green/white, etc.
Data is usually carried over 2 pair, and the other pair are unused in most applications. So the unused pair get power. There are certain variances to this depending if you are using POE, POE+, etc but that's the jist. There are also different voltages but that should not be relevant for this project.
As explained above, 4 pair come into the injector, and power/voltage is applied to 1 or 2 pair. Most devises are auto sensing, so if you plug a laptop into a POE port on a switch, the switch will not turn on PoE and will just pass data. Injectors usually arent as smart, and just pass power regardless, so be careful and make sure you check your ports LAN/PoE before plugging stuff in.
PoE is PoE regardless if it comes from an NVR (IP devices use NVR's not DVR, Network Video Recorder versus Digital Video Recorder), switch, or injector. But the device has to be PoE capable. Not all switches are PoE capable, and they are more money.
Most of your consumer NVR's have ports built into them that are POE to keep it easy to use and manage. On commercial projects, we hate it and only use PoE switches.
The laptop is irrelevant and the OS should not matter, except for the software. The SW may not work on Win 8, but you should still be able to do everything you need from a browser. You should be able to access the NVR via a browser.
I will say the camera you have is manual zoom which means manual focus. Those are a PITA to adjust. There should be two screws, one for zoom, and one for focus, and the focus is usually down to hairline adjustments. We only use motorized lenses, and they are not that much more.