Personal terms are the parts of a transfer agreed between the club and the player rather than between the two clubs: wages, contract length, bonuses, image rights and any release clause. A deal needs both, so a fee agreed between clubs still collapses if personal terms cannot be settled.
Two negotiations run alongside each other in any transfer. Clubs settle the fee and its structure; the player, usually through an agent, settles what they will earn and under what conditions. Either can fail on its own, and that is how a transfer gets reported as agreed and then quietly dies.
The sticking point is often not the headline wage. Contract length matters for a player near thirty, bonus triggers matter for a forward, and a release clause matters for anyone joining a club they see as a step rather than a destination. A club with a rigid wage structure will trade on those before it breaks its salary bands.
Personal terms can legitimately be discussed before a fee is agreed if the current club has given permission, and cannot be if it has not. Opening those talks without permission is tapping up, which is a disciplinary matter rather than a formality.