Sunspore,
A browser is a piece of software for viewing websites. In your case IE is your browser, but others are around. Some you may have heard of are Mozilla, Netscape and Opera.
ISP's (Internet Service Providers - companies that provide access to the internet) can customise internet explorer quite easily, adding their own name and logo via a piece of software available from MS.
This is why you often get "Internet explorer provided by XYZ" in the title bar when installed from ISP CD-ROM's.
As for emails, they are normally in one of 3 types: plain text is exactly that. No flashy images, graphics, fancy sounds. For many years this was the only method and even now, many clients don't support anything more. There is a school of thought by many that says if it can't be said in plain text it shouldn't be said at all, as using the other methods significantly increases the size of transmission and download over plain text.
HTML email basically uses HTML (HyperText Markup Language, the 'tags' used to turn plain text into word documents) to spice up emails. They can therefore have sounds, images, multiple fonts and different colours etc, and are often rendered by a web browser application.
The other one is Rich Text, which is a similar idea, but doesn't (to my knowledge) support graphics. It is less flexible than HTML.
Any emails with embedded images are likely to be in HTML, and you will need a client that supports it. With Internet Explorer, Microsoft supplies a well known email client that does called Outlook express (as distinct from the full blown Outlook supplied with Office) which will do this for you.
I hope I haven't blinded you with science here...
John