OK this might help a bit....
You need somewhere online (a 'website') to store your info for others to look at. If you want this website to have a custom name, for example 'the-smith-family-history.com' you need two things:
1 A domain name (the 'location'
www.the-smith-family-history.com for example).
2 Some web space to 'host' or simply 'hold the content of' your domain name.
You mentioned the company 1&1 - they can sell you a domain name and provide space to use with that name. You can also register a domain name with one company and have it hosted on another.
For example I 'bought' the domain name
www.digdeeper.org.uk off one company (I think it cost a couple of pounds for two years) but host it with another company (that costs about £30 per year in this particular case).
So, assuming you have a domain name and some webspace - you now need some family history software to display (and maybe edit) your data.
In simple terms, you install this program to your webspace, upload your data to the same webspace and away you go.
Using a 'service' like Tribal Pages or Ancestry.com removes the need for buying a domain name or renting web space - they do all that for you, you just upload your data and off you go. The disadvantage of using a service is that you're stuck with their way of doing things and so don't have full control of your data and what happens to it.
Hope that's some use, shout if you need further explanation!
Paul