Tapping up is approaching a player who is under contract at another club, or their representatives, without that club's permission. It breaches the rules of most competitions, which require a club to notify the current employer before opening talks, and it can bring fines or transfer sanctions.
The rule is easy to state and hard to police. Almost every transfer involves an agent who has spoken to several clubs, and the line between an agent offering a player and a club approaching one is thin enough that most cases never produce evidence.
Charges therefore tend to follow something written down or said in public. A manager naming another club's player admiringly in a press conference is the version supporters see, and it is enough to draw a complaint even when nothing improper has happened behind it.
The rule exists to protect contracts rather than to stop transfers. A club that wants a contracted player is expected to ask the club first, get a yes or a no, and negotiate from there, which is what a formal bid is for.