What Klaviyo adds, and where
Klaviyo, an email and SMS marketing platform, says in its help center that it "adds a parameter, known as the _kx parameter, to all URLs in your email or SMS message to track activity." The sender does not add it link by link. Klaviyo appends it automatically, so a link from a store's Klaviyo newsletter or text message is where you will find it.
An encoded ID for the person who clicked
Klaviyo calls it a "unique encoded parameter" that its web tracking decodes to "identify the user that clicked through the URL." In Klaviyo's own example the value is J8fjcn003Wy6b-3ILNlOyZXabW6dcFwTyeuxrowMers%3D.McN66. Your email address does not appear in it as plain text. Klaviyo's script on the store's site decodes it. When the store has email-to-website tracking switched on and Klaviyo's tracking snippet installed, Klaviyo identifies and sets a cookie on people who click through from an email or SMS and browse the site.
Why it matters when you share a link
Because _kx is what tells the store who clicked, a copied link carries that with it. Paste it into a group chat, and anyone who opens it on that store could be recorded as you in the store's Klaviyo account. mc_eid on Mailchimp links and mkt_tok on Marketo links carry the same risk. Strip it before a link leaves your own inbox.
What the store loses
Klaviyo says the parameter will not slow the page or break the URL, and removing it does not either. Nothing changes on screen. What goes is the store's ability to connect that visit to the subscriber who clicked. Store owners can toggle email-to-website tracking on or off in the account's email settings.