The answer to this can get really complex and depends on how deep you wish to go.
Text is there for a user to read and therefore should be readable, (just so happens google use it as well) The variable part though is screen size and resolution. This is the same for mobile and desktop. So on some devices, 16px could seem huge but on others impossible to read.
This is why using px is not recommended as that measures the font in pixels, the correct way is to use REM.
Now although this was not part of your question it is also related, that is font colour (or color, depending on where you live) Text should have sufficient contrast to also make it easy to read. Failing on this can have a negative effect.
There used to an old black hat technique where you put small text in white on a white background to stuff your keywords into a page. The user would not see the text but google would and used to rank you for that text. To combat this they do take contrast into account to confirm the text is visible.
A technique I have not seen to quite a while now is webmasters used to offer impaired vision users a high contrast skin to their website. Its quite a bit of extra work for the webmaster so it seems it's now gone out of fashion and now depend on users to install plugins to achieve the same result.
As a webmaster I know its always a battle between designers and SEO, style tends to win to begin with until the owner starts moaning that rankings are not where they should be. So if your starting a new project and can offer input into the design then make sure the text is easily readable on many devices and where possible even users with sight problems.