Anything required is mandatory or needed. If something is required, it's not optional. You better do your required reading over the summer, or else...
To require something is to demand it, like a restaurant requiring men to wear a jacket. Anything described as required is similarly demanded by some person or organization. A license is required to drive. A credit card is required to get a hotel room. A helmet is required in football. Sometimes this word is used more loosely. For example, a glass of water will be required for most people after a workout. That just means the water is needed.