"Heart Lock" / "Heart locking" is a feature in Kantai Collection that is used to protect a ship girl from being accidentally scrapped or used as modernization material.
When enabled, a heart with a lock icon will appear on the right next to the girl's entry on various screens and menus (commonly seen on the fleet management screen when one is shifting girls around). This means that if you try to send the girl to the scrapyard or use her for modernization, the Confirm/OK button will be disabled.
Note that it will not protect the ship girl from sinking if she is downed/sunk (HP <= 0) after entering combat with an red HP bar. This "heart lock" feature is intended as a safeguard for a player to prevent scrapping of, for example, a married Lv 99 Haruna that is in the players' fleet.