Soft Constraints are a type of constraint that can be violated in obtaining a feasible solution, but violating the constraint can have a negative impact (i.e., like a penalty) on the solution compared to if it wasn't violated. Said in another way, a soft constraint guides the decision process but can be ignored / broken if necessary.
Soft constraints need a sensitivity score to determine the impact (penalty) of each constraint to the impact on the goal. If there are too many soft constraints, the challenge will become hard to solve because there will be many ranges to test simultaneously, and the solution becomes very large and slow.