One reason for a micro site was to try to get ranking on a search term quickly. In this case a micro site was a small site with a keyword in the domain name.     The concept took advantage of the weight that search engines use to put on keyword matching domain names. So if you wanted to quickly rank on “plastic toy trucks”, you would buy the domain name plastictoytrucks.com or even plastic-toy-trucks.com and throw up a couple page website.   With minimum link building one use to be able to achieve top 10 rankings in a very short period of time.
Some companies took this concept to the extreme by buying thousands of domain names and creating thousands of small sites.   This was a very common technique for national companies that wanted to rank in specific geographic areas. So a locksmith company would buy domain names that started with “locksmith” and then included a city that they wanted to dominate in; locksmith-detroit.com would be an example. The content on each of these sites would be adjusted for the geography it appeared in.  
I know of one SEO firm that use to use this technique exclusively.   They would buy a keyword matching domain name, put up a graphic page as a one page website and charge the client a monthly fee for that site.   I assume that SEO firm is out of business because they will get a lot of disappointed clients buy doing that today.
This technique use to work a couple years ago, but it not anymore.   Most micro-sites that were built for this purpose had very low quality content and were discounted by Google’s recent panda updates. Also the weight that Google places on keywords in the domain name has been significantly discounted.   One can still find a lot sites with exact match domain names ranking well for that term, but those sites are usually not micro-sites and the site has other aspects that affect ranking such as domain age, incoming links or solid content.   There may even still be some micro-sites ranking that are remnants from years ago, but the strategy of building a micro-site to catch traffic is pretty much a waste of time.
 You may see this still working on long stem keywords that have no competition.   The traffic that a site might get for that is miniscule and the conversion rate would be zero. One would be far better off investing time working on the main site. Adding a high quality page to a larger site will gain more traffic faster than creating a micro site.
Another SEO purpose for micro sites was to create a bunch of sites that would link to some target site for the purpose of increasing rank for the target site.   This technique hasn’t worked for several years and is a very dangerous practice because it can get your site banned from Google.
Setting up a new website with a common keyword in the domain name is still helpful because studies have shown that a SERP listing where there is a keyword in the domain name has a higher click through rate. But other factors such as brand identity, convenience and ease of remembering are as important. Quite frankly, most domain names that would match competitive keyword phrases are probably taken or would sell at a premium.