Hi there,
From you're post heading and content I'll cover both aspects -
1. 'Mobile Broadband' - When this term or phrase is used, it refers to being able to access the internet at broadband like speeds when out and about, i.e out of the house. Just like a mobile phone is used to make voice calls all over, mobile internet means you can access the internet all over (both theoretically!)
2. If you want to be able to have Internet at home and accessible from various rooms in the house, then the most common way is to use what's already been suggested a Wireless Modem/Router. You'll need to order a broadband service from an ISP that's enabled on your home telephone line, once done, you connect the router to it and a wireless signal is transmitted so that the laptop you buy this weekend can pick up the signal and you can check out the latest bargains online whilst sitting outside with yer shades on in the sunshine!
That's both aspects in a nutshell, there's quite alot of info over on
www.thinkbroadband.com and have a look at pcpro.co.uk and computershopper.co.uk for reviews on various bits of kit. When wireless works nicely it's great, but it can be a pain in the jacksie if there's problems although mostly 'treatable'!
if you have any queries mention them here and I'll see what I can suggest.
Overall, you shouldn't have too much of an issue to get what you want - just some time spent shopping around to get the best deal to suit your pocket!
Cheers, DtM! West London & Slough UK!