What si actually is
si is a share identifier, and you meet it most often on YouTube and Spotify links that came out of a share button rather than being typed. It identifies the share that produced the link, which is how a platform can tell that a burst of traffic all originated from one person passing a link around.
It is short, opaque and easy to miss, which is why it is one of the most commonly pasted-without-noticing parameters on the web.
What it does and does not tell people
It does not contain your name or account details. It does allow the platform to associate visits with the share event that created the link, which in practice means a chain of people who all opened your copy of a video can be recognised as connected. Whether that bothers you is a judgement call, but there is no cost to removing it.
Is it safe to remove?
Yes, on the platforms where it is a share token. One caution worth stating plainly: a two-letter key like si is short enough that some other site could legitimately use it for something functional. The decoder above strips si wherever it appears, whatever the site, so if a link from anywhere other than YouTube or Spotify stops working after cleaning, put si back.
The related one
On YouTube you will also see feature, which records which surface of the app the link was copied from. Same family, same harmlessness, same lack of any reason to keep it when sharing.