A pre-contract is a binding agreement a player signs with a new club while still under contract elsewhere, allowed once their existing deal has under six months left. The move itself happens when the old contract expires, and the new club pays no transfer fee.
The six month line comes from FIFA's transfer regulations, which let a player conclude a contract with another club once their current one is within that period of expiring. Until that point an approach needs the current club's permission.
Domestic rules vary on top of it. Some associations allow clubs in the same country to agree pre-contracts on the same basis, others restrict it, which is why the best known pre-contract moves tend to be across borders and why Scottish football in particular is associated with the term.
For the selling club it is the worst outcome in the market: a player they can no longer sell, running down a contract in public, with a destination already settled. That pressure is why clubs push so hard to either renew or sell in the summer before a final year begins.