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',
h(n)<=(n,a, n’)+h(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:
h(n)≤h∗(n).