What mc_eid actually is
mc_eid is Mailchimp's email ID, and it identifies the individual subscriber who received the campaign. It almost always travels with mc_cid, the campaign ID, and the pair answers two different questions: mc_cid says which email this was, mc_eid says which recipient. Only one of those is about a person.
Why this one deserves more care than most
This is the parameter people accidentally leak. You click a link in a newsletter, land on an article you like, copy the URL from the address bar and post it somewhere public. The address you copied now contains a token tied to your subscription. It is not your email address in plain text, but it is a stable handle for you within that sender's list, and it does not belong in a public post.
Other email platforms have direct equivalents worth recognising: _hsenc for HubSpot, mkt_tok for Marketo, _kx for Klaviyo. Same shape, same caution.
Is it safe to remove?
Yes, and it is the one you should remove by reflex. The page works identically, and stripping it only means the sender cannot attribute your specific click. Use the cleaned link above any time a URL from an email is leaving your own browser.