Intensity is often used just as a non-technical adjective. "I worked out with a lot of intensity." It's used much like "hard" or "heavy" - "I worked out hard and lifted heavy" can mean different things to different trainees.
The technical definition of intensity is more specific.
The intensity of a lift is the percentage of your one-rep maximum. The maximum weight you can lift only one time is considered a lift at 100% intensity. From there, it's simple math - a weight 75% of your 1RM is at 75% intensity.
For cardiovascular training, intensity is measured as a percentage of your maximum heart rate. A run at 50% of your maximum heart rate, even if it's your best time for the stated distance, is lower intensity than one at 80% of your maximum heart rate.
Intensity is something used in a less technical way, to describe how hard the effort made by the trainee is for that trainee. If the trainee pushes to the limit, attempting to set a new PR, work until you drop, run at full speed, etc. the work is considered high intensity or going 100%.
As you can see, intensity can be somewhat of a slippery term.
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