You understood admissible heuristic very well. Now coming to the concept of monotonic property, In the context of search algorithms monotonicity (also called consistency) is a condition applied to heuristic functions.
A heuristic h(n) is monotonic if, for each and every node n and every successor n' of n generated by any action ‘a’, the estimated cost of reaching the goal from n is no longer greater than the step cost of getting to n' plus the estimated cost of reaching the goal from n',
Because every monotonic heuristic is also admissible thus the monotonicity is a stricter requirement than admissibility. Some heuristic algorithms such as A* can be proven optimal provided that the heuristic they use is monotonic.
The heuristic function h(n) where,
h is admissible, if for all nodes n
n in the search tree the following inequality holds: