Merit accrues to Individuals through their visible and productive work within a community. To put it another way, merit is the invisible currency that you gain by contributing useful work to the project. There are a number of common aspects to merit as it's recognized within The Apache Way, the most important one is it's recognition by the community. You don't gain merit by simply doing a lot of work; you gain merit by doing things the community values.
The most obvious reward for your merit is being voted in to be a committer within a specific community. The merit level to become a committer varies from community to community; it can span anything from a handful of useful patches and helpful questions on a mailing list, to several months of sustained hard work on the code, mailing lists, or website.
Within the ASF, most projects have fairly similar processes for actually recognizing merit. The specific processes are specific to the ASF, but in many cases are echoed in other open source projects as well.
Committers have write access to their project's code repository. This means they may directly contribute to the project's code, website, and other materials. Committers who continue to show merit may be recognized by voting them onto the Project Management Committee (PMC). PMC members have binding votes on the strategic direction of the project, and on making formal releases. One PMC member is typically voted in by the community to become the chair of the PMC, and with that comes the role of Vice President of that particular project.
Note that within the ASF, voting in committers is done solely by each project's PMC individually; they act independently in this respect. When voting individuals onto the PMC itself, the Board of Directors of the ASF exercises oversight, and approves all PMC changes by a simple 'ACK' email. The Board also specifically passes resolutions at monthly meetings to appoint, remove, or change Vice Presidents of Apache projects.