Any electronic device with a service or update plan will inevitably have an end of life, even if it's far off in the future. At that point, updates and support for the device will stop. For most smartphones on the market, that end of life period is anywhere between 18 months and two years after release. For Chromebooks, there actually was not a concrete end of life until 2013, when Google put out some rough guidelines for end of life on Chrome OS devices. Recently, that end of life policy posting was updated with a chart detailing different Chrome OS devices and their end of life dates. In fairly ambiguous terms, that policy essentially says that Chrome OS devices reach their end of life 5 years after release. Until then, they are guaranteed security and feature updates on a regular basis, specifically every six weeks.
In Google's policies, Chrome OS devices will receive automatic updates until the end of their life cycle, at which point the updates are "no longer guaranteed". Likewise, "full support" for Business and Education customers' devices is not guaranteed, and management features for them in the Admin Console may cease to function. The definition of "full support" is, of course, not given. Chrome OS devices in this category are considered to have an "unofficial" end of life at the moment, which could be subject to change. If these dates change, fortunately, they will end up further in the future, rather than sooner.
Reaching the end of life is not a guarantee of obsolescence, per se. While devices five years old and older are certainly outdated from a hardware point of view, Chrome OS' lightweight nature and the relatively powerful hardware out today, and even as far back as 2011, mean that these devices can still be used for lightweight tasks well into the future, so long as they're kept in working order. That may not be recommended, though. When a device reaches its end of life, it is no longer guaranteed updates. While Google and the manufacturer may continue to push updates to it, the latest features and security fixes may end up missing the machine, leaving it not only functionally hobbled compared to newer devices, but less secure as well. Security patches incorporating known vulnerabilities from both high-profile hacks that make the news and findings from such hacks ending up in these patches, which means your older device may end up vulnerable to a bug that's been widely reported on and is easy to reproduce at that point. Naturally, aside from grabbing a newer build manually, which may or may not be possible, the only alternatives at that point are to move over to Linux if your device is able, or to replace the device.