It's really simple.

Google is in most countries. If someone in South Africa searches in Google for "buy new ipod", it would be more relevant for Google to offer local suppliers. Some countries have rules which makes it harder or more expensive to get a local domain than a global one. For local search queries sites which match the local domain extension or are hosted on a machine in that country may get a boost in relevancy over global domains. For example, .co.uk may rank well in UK, .de may rank well in Germany.

Google can use the increased price of local hosting and/or the rules associated with gaining a local domain extension to assume that locally hosted or locally registered domains may have a greater local relevancy.

Likely due to less spamming incentive, a smaller content base, and a lesser understanding of local language many of the filters that are applied to the global search results may not be applied to some local results.

Beyond .edu and .gov there are also other rare domains which people probably do not talk about that much which also have similar importance. In the UK .ac.uk is the equivalent of a .edu, and perhaps some .mil extensions may be trusted a bit more than the average .com, .net, .info, or .biz type domain.

The factor of trust would be three fold:

• The standards required to get a .edu or other rare domain extension implies a certain level of credibility.
• Generally much of the well cited college papers or governmental pages are of higher quality than the average web page due to internal requirements. On top of that they are harder to influence than most average web pages. For example, it is pretty damn hard to get a professor to link at your site or update his or her outdated links. No professor wants some random self promotional asshole (which is how they will view many people who contact them) telling them that their content is outdated or inaccurate.
• When the web started educational institutions and governmental bodies were at the core of it. Thus, with greater history, they are more likely to have more link equity. Over time webmasters of scraper sites and legitimate web pages are going to be more inclined to link at the top ranking pages, which reinforces the link popularity.