Origins
An intense person is, etymologically, stretched to breaking point.βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ The word comes from Latin intensus, the past participle of intendere β 'to stretch out, to strain' β from in- ('into') and tendere ('to stretch').
The image is a bowstring drawn taut. Anything intense has been pulled beyond its resting state: intense heat, intense emotion, intense concentration. The physical metaphor of stretching underlies every modern use.
The PIE root *ten- ('to stretch') generated a vast family. Tend and tendency describe the direction something stretches towards. Attention is stretching the mind towards a subject. A tent is stretched cloth. Pretend is stretching something forward as a front. Tender meat yields easily to stretching. Tendon is the body's stretching tissue.
Latin Roots
Intend preserves the root meaning most literally: to intend is to stretch your purpose towards a goal. Latin intendere meant exactly that β to direct, to aim, to stretch one's will.
The word intensify appeared much later, in the 18th century, as science needed language for increasing degrees. But the core metaphor has not changed since Roman times: to be intense is to be stretched tight, fully committed, pulled towards something with no slack left.