The campaign, not the reader
Mailchimp's developer documentation puts it in one line: "The mc_cid parameter is the Mailchimp ID for the campaign that generated the link." It names the send. Everyone who received that campaign and clicked the link sees the same mc_cid.
The parameter usually sitting next to it works differently. mc_eid, in Mailchimp's words, "identifies the recipient's email address." A link with both tells the site which newsletter sent the visit and which subscriber clicked.
What a store does with it
mc_cid exists so revenue can be credited to an email. When a store adds an order through Mailchimp's e-commerce API, Mailchimp tells developers to send the mc_cid value as the order's campaign_id, which marks the order as coming from that campaign. For campaign revenue tracking, Mailchimp requires orders to include campaign_id, processed_at_foreign and financial_status. If a redirect drops mc_cid before the store reads it, the order has no campaign to credit.
Its product recommendation cousin
Mailchimp adds one more parameter to some links. When a reader clicks a recommended product in an email, the link includes mc_tc, and the store sends that value as tracking_code to credit revenue to the recommendation. A link carrying mc_tc came from a product recommendation in a Mailchimp email.
Which half to strip before sharing
Removing it does not change the page. On privacy, mc_cid is the low-risk half of the pair, since it names a campaign sent to a whole list. The one to remove before you post a newsletter link in public is mc_eid, which ties the link to your subscription. The decoder above gives you a copy with both removed. Other email platforms have their own versions of mc_eid, such as _kx for Klaviyo and _hsenc for HubSpot.