Sensitivity reflects the proportion of true positives (on some criterion variable) that a given indicator flags as positive. A value of 1 indicates that every true positive case was so identified/flagged by your indicator variable.
This could occur if:
1. The indicator scores are genuinely indicative of and highly corresponding to true status (this is the ideal case; the others which follow are not).
2. All cases were true positives, in which case the indicator scores don't necessarily have to relate to true status.
3. You have a very small sample size.
4. The indicator variable is actually redundant with the true status measurement (for example: if the indicator variable was BMI score and the true status was whether or not a case was classified as morbidly obese).
Less than one means parameters are robust. Greater than one means it is a sensitive parameter i.e one that elicits a large change in model output for a small change in a given input parameter :)