"I have just had TalkTalk fibre broadband installed. They supplied me with a Huawei router. It seems better than the BT HomeHub I previously had, but I don't like it and it doesn't have gigabit Ethernet ports on it. However, it does have a USB socket that allow a memory stick or external hard drive to be shared, which sounds a good idea. Two questions: Do I have to use this router? And if I do, will the shared USB drive be the same as a NAS?"
The short answer is: no, you don't have to use the TalkTalk router at all. The Huawei HG533 that TalkTalk commonly supply is widely regarded as one of Huawei's best efforts to date, but will not suit everyone. But you can simply replace it with just about any router of your choosing. TalkTalk's fibre, like any other company's, actually connects using a BT Openreach modem. This, in turn, connects to the Huawei router using a standard Ethernet cable. As long as your alternative router has an Ethernet socket on it - and they all do - then you simply plug it into that instead. Domestic internet routers come in two flavours: for use with cable connections and for use with ADSL ("telephone line") connections. For best results, you want a cable router (ADSL can be made to work but is more fiddly). The really good news is that TalkTalk fibre broadband doesn't use any passwords or have odd settings - it really is just a matter of connecting the modem to whatever cable router you fancy.
With regards to the second question, many home routers come equipped with USB ports that allow an external hard drive to be shared (besides the Huawei there is the BT HomeHub 3, the Apple AirPort, Western Digital My Net N900, models from Belkin and Netgear et al). Typically the drive will appear as another disc volume, for instance it might appear as the Z: drive or something. Alternatively, you might have to type something like \\192.168.1.1\shared to access it. As every computer in your household/office can see it, it potentially gives you a mechanism to share files and folders.
However, in practice these facilities often don't work very well at all. The processor in a small router is not very powerful; often it cannot adequately cope with the demands of serving up the internet and files at the same time. If it can, performance may be very poor, for instance you may only be able to read or write files at a lowly 1Mbyte/sec or so. There may be few or no controls, with no concepts of privacy and security. It may prove flakey, with dropouts. It might be the case that only certain external drives or USB memory sticks will work with it. So, for these reasons, the shared storage facility offered on routers is not very good and it is better to go with a conventional NAS drive. An alternative for some people who may already have a USB drive that they were thinking of using is the Synology USB Station 2. This is a small, silent version device that has no storage of its own; instead, you bring your own. It costs around £80 and more information can be found here.