The 15 degree rule refers to the measurement used to determine if a bowler is following the rule against throwing the ball. It’s not used during games but is used during external assessments.
The Laws of Cricket say that bowlers must not throw the ball and that once their arm reaches the highest point of their delivery (ie pointing straight up), they cannot bend their elbow at all until they let go of the ball. For many years this was enforced solely by the umpires during the game. If they spotted a player bending the elbow, they would declare a no ball.
When games started being filmed with techniques such as high definition and slow motion, it became clear that virtually no bowler literally follows this rule. Instead there is almost always a small degree of bending that is difficult to spot in person in real time.
The ICC then introduced a rule that says umpires can report a player they suspect of habitually breaking the law on bowling action. The player will then be called for independent assessment of their bowling action. This involves video analysis of their delivery, measuring the angle that their elbow bends before releasing the ball.
Originally the maximum angle allowed varied depending on the preferred style of the bowler (eg spin or pace). Today the same threshold of 15 degrees applies to all bowlers.
To visualize this, imagine the bowler’s arm is straight and upright and resembles the hands on a clock showing 6 o’clock. The 15 degree limit is equivalent to the hour hand moving to half way between 12 and 1.
If a player consistently breaches this threshold in the independent assessment, they will not be allowed to bowl again until they have adjusted their standard delivery technique and a fresh assessment shows they are within the threshold. The ban applies to games regulated by the ICC and by the relevant national cricket organisation in the player’s country.
Critics of this approach say it is unfair because by the time a player reaches a high enough standard that video analysis is available to show their action breaches the rules, it is often too late in their career to change their natural habits and techniques.