Search engine marketing
Search engine marketing is the whole shebang of online activity intended to get your product in front of eyeballs and make sure it sells.
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Competitor Analysis
By 'competitor', search engine optimisers mean 'a company at the top of the search engines for the phrases you want to rank well for'. 'Competitor' doesn't mean 'a company with a shop next to yours who sell the same things you do' - except in the sense that one of your keyphrases might be 'widgets for sale in anytown' and they are ahead of you in the search engines for that phrase.
Who is linking to your competitors?
One of the principle activities in this field is to check where your competitors are getting links from. Since Google ranking is mostly powered by links, this takes a high priority. If you can get links to your site from the same places your competitors do, then you will be a long way down the road to emulating their success.
If they have been carrying out SEO work themselves, you can also pick up new angles on keyword selection from their activities - whilst an SEO can be very good at finding out the mainstream keywords for a certain type of business, there are always specialist words that can go unrecognised. Competitor analysis can help shake loose these words and phrases for inclusion in your own efforts.
Are your competitors offering more than you?
There may also be certain things that their website offers which helps them to draw in traffic. This could be something as simple as sending out a newsletter, or they have an representative for online activities such as blogging, or writing a newsletter, or maintaining a presence in certain fora. Perhaps they offer an online glossary - a glossary is a great way of legitimately covering a lot of keywords, and offering your visitors something useful at the same time. It also encourages deep-linking into your site
Finally, it is very dangerous in SEO to think that the way search engines rank websites is static - it changes all the time. With this in mind, an SEO will also look at the ways top sites are optimised and learn from them. However, this is more part of being an SEO, not part of looking at what your competitors are up to. Generally speaking, the main activity of competitor analysis is finding out where they get their links from.