I worked for Apple for 7 years and just changed jobs 3 weeks ago.

I'm going kinda basic here... apologies if any of this is goofy simple.
Mac is short for Macintosh. Get it? Macintosh is a type of Apple. The first Macintosh was released in 1984. All of Apple's computers since then (if we don't split hairs) have been called Macs. As Randy mentioned, they're not MACs, since this would imply that MAC is some sort of acronym, which is isn't. The operating system that runs on them is called Mac OS. For the past five years, The operating system has been called Mac OS X (roman numeral ten). There have been several versions of Mac OS X over the years. They all have cat codenames: puma, jaguar, tiger, panther and soon Leopard (version 5).


The Mac is great for document writing, and it's the best thing available for work with photos or video.

Before I dig in, I should explain some terms you might want to know...
Microsoft Office- This is virtually the same as the Windows counterpart, except instead of Outlook there is a semi-equivalent product called "Entourage" for mail. Also, there's no Visio or MS Project equivalents produced by Microsoft for the Mac. btw... I don't recommend using Entourage for mail. Use Apple's mail application. It's much more stable.
iWork- This is a software suite produced by Apple that includes a presentation app called Keynote that is similar to Powerpoint as well as a document writing app called Pages which is similar to Word. Both are a little thinner on capability and features in some areas (Pages in particular), but they produce prettier results. trivia... Keynote was developed for Apple CEO Steve Jobs. He was sick of using Powerpoint for his presentations, so his developers made Keynote for him. That's why it looks good. Eventually he decided to release it as a product. To get an idea what is possible with it, watch one of the MacWorld keynotes.
iLife- iLife is where the core value of a Mac lies, imo. It's comprised of iTunes, iPhoto, iMovie, iDVD, iWeb and GarageBand. iTunes manages your music library pretty much exactly like Apples Windows version does. In addition, you can use songs from your music library in iPhoto, iMovie or iDVD. iPhoto manages your photo library pulled from your digital camera or other sources. iPhoto also enables you to load pictures onto your iPod, order picture books, greeting cards, posters, etc, enhance your pictures and do some basic effects, create slide shows, etc. It also can work with iMovie and iDVD to integrate your pictures into your movies or DVD menus. iMovie enables you to capture and edit digital video. You can also incorporate pictures or music from either iTunes or Garageband. iDVD enables to you burn DVDs of your movies or photo slide shows. Garageband enables you to compose your own music using multiple tracks. You can either play your own instruments or work with hundreds of digital instruments and samples built into the application. iWeb is a fabulous application where you can create your own web sites to display all of the pictures, video and audio from the other iApps. All these applications are simple enough that you can start using them effectively without reading a manual. I don't know how they do that, but it's really true.
iChat- Apple's own AIM client. Enables the user to communicate over AIM through text, audio or video with an iSight.
iSight- Apple's webcam. There are standalone units as well as units built-in to all recent computer models. Works with iChat.
Mail- Apple's mail application
iCal- Apple's calendar application
AddressBook- where you can store your friends' contact information
iPod- where your content from iTunes, iPhoto, iMovie, GarageBand, iCal and AddressBook go.

Document Writing
There are two main options. The first is Word in Microsoft Office. This is probably your best bet for documents that need to be pure text or sent/shared with others. If you need documents that look good with lots of captivating graphics, flyers, pamphlets, etc, Pages, which is part of iWork, is really snazzy. It's wuite a bit different than Word and takes some getting used to, and it's not as powerful for lots of text, but for a combination of text and graphics, it produces some beautiful results. I have used both virtually equally. I use Word for my documents I produce for my job, and I use Pages for documents I produce for personal things, like letters and, in particular, stuff relating to my upcoming wedding.

Photos
iPhoto is hands down the best consumer-level product out there for storing photos on any platform. It does exactly what you need it to. It also has some basic photo manipulation tools, including enhance, airbrush, redeye remover, effects, crop, etc.

Movies
iMovie. Same thing here. Lots of effects, transitions, the ability to add two audio tracks, etc.

Other stuff to mention
Other tidbits useful to know...
Since Apple came out with the Mac OS X operating system there have been less than 30 viruses developed that attack Mac computers. Somewhere between 5% and 10% of computer users use Mac OS X. In contrast, Windows XP has thousands of viruses. About 85%-90% of computer users use Windows. Thousands of viruses have also been developed for Linux. In other words, Mac OS X is far less likely to get messed up from viruses than Windows.
All current models of Macintoshes can run either Mac OS X or Windows. They can even run both at the same time. You can have a Mac OS X application running in one window and a Windows application running in another window. Macs also can run Linux. So, in theory, you could have applications running on three different operating systems all running at the same time in different windows. A non-Mac computer can't do this. So in this sense, Apple is the most compatible computer out there right now.

Apple produces the following Mac computers:
Mac Mini- Apple's most basic model. The "entry" desktop model. All it is is the box itself. (and it's tiny) It doesn't come with a keyboard, mouse or display (most people have these already).
iMac- Apple's "consumer" desktop model. The computer components are built into the display, so there is no box... just a display, mouse and keyboard.
Mac Pro- Apple's fancy "pro" desktop model. It comes with a big box made of aluminum, a keyboard and a mouse. These are very high end with a price to match.
MacBook- Apple's "consumer" laptop. Comes in Black or white.
MacBook Pro- Apple's "pro" laptop.

What's the difference between "entry", "consumer" and "pro"? Entry is the most basic, Pro is the fanciest. Consumer is in between. This refers to features, capability, capacity, and price.

So I hope this is a good primer to get you started, so that you can make an educated buying decision. I would suggest making your next stop at the closest Apple retail store. Apple's retail stores have become known in the retail industry as having the most knowledgable sales staff and best display of electronics pretty much anywhere. There you'll be able to see all of the models mentioned above in action with other devices connected to them in various ways, with all kinds of software, music, movies and photos installed, etc. You'll have a good chance then to ask any additional questions to the staff there, and, believe it or not, they will not only be available and ready to help you but are likely to have a good answer for you. One word of caution... the stores get crazy busy on weekends. It's much more peaceful during the week.

Bonus... you can find an example web site I made for my mom using iWeb here. I did it in about 45 minutes. ^