Two solid rocket boosters are used during a shuttle's launch - one to the right and the other to the left of the external tank. Because the SRBs are reusable, both Morton Thiokol (their maker) and NASA (their user) could test how they performed during launch. Although they appeared to perform well (to those not on the inside track), the solid rocket boosters had a fundamental, potentially fatal design flaw.
A solid rocket booster and its solid rocket motor are made separately. The booster and the motor become a single unit when their sections are joined together. Before the Challenger disaster, it was the joining of those sections - in the joints themselves - where prior problems during tests and actual shuttle flights had been noted.
The primary culprits were the rubber "O-rings" used to seal joints. Especially in cold weather, the O-rings had a tendency to erode. When they eroded, they could no longer completely seal joints. Unsealed joints could set up potential failure modes. Morton Thiokol and NASA knew that before the Challenger disaster.
Eroded O-rings led to misaligned ("rotated") joints. Misaligned joints led to undesirable things like exhaust gas blowing through, and out of, the solid rocket booster. Exhaust gases must be kept away from the shuttle's external tank (which contains liquid hydrogen and liquid oxygen). If the rings were not properly sealed, gases would escape. Morton Thiokol and NASA knew that before the Challenger disaster.
Erosion of the O-rings had been noted by Morton Thiokol and NASA after other shuttle missions. Because the rings had not failed, however, officials decided the erosion was an "acceptable" flight risk.
As the President's Commission investigating the disaster and its cause later noted in the official report, chapter 6, the Challenger disaster was:
An accident rooted in history.
And what a terrible history it was.