The process for article selection for offline releases of Wikipedia is now mainly automated. It is specifically used for assembling the so-called release versions; the next release (as of September 2011) is called Version 0.9.
The User:WP 1.0 bot collects information about quality and importance of articles for these WikiProjects. These data are then used to rank articles based on a combination of quality and importance (as described below), and articles are selected based on these rankings. To ensure that nothing is overlooked, single articles can still be nominated manually then reviewed. This approach has been used for all releases beginning with Version 0.7 (31,000 articles).
The bot computes a numeric score for each article. Articles that have a score over a certain threshold (which will change from one release to the next) will be included in the release version. The threshold for Version 0.8 has been set at 1240. This page describes the algorithm that the selection bot uses to assign scores.
Older tests are described at Wikipedia:Version 1.0 Editorial Team/Selection trials.