Not all plugins can work on PHP 5.2, like WordPress core currently does. Not all plugin developers want to support PHP 5.2, like core does. As a project, WordPress would like to move forward and encourage people to use more recent PHP versions.

As one of the first steps to reach that goal, plugin authors can now specify a minimum required PHP version for their plugin in readme.txt file with a new Requires PHP header:

=== Plugin Name ===
Contributors: (this should be a list of wordpress.org userid's)
Donate link: http://example.com/
Tags: comments, spam
Requires at least: 4.6
Tested up to: 4.8
Requires PHP: 5.6
Stable tag: 4.3
License: GPLv2 or later
License URI: https://www.gnu.org/licenses/gpl-2.0.html

Users will see this displayed in the plugin directory, like this:

As a next step, the WordPress core team is going look into showing users a notice that they cannot install a certain plugin or theme because their install does not meet the required criteria, with some user-oriented and host-specific instructions on how to switch their site to a newer PHP version.

If you have any feedback on the subject, please leave a comment or join the next PHP meeting in #core-php channel on Slack.