Could somebody please explain me what kind of expenses are the "contingency expenses" for example in the monthly reporting (finance)?

Contingency (similar to emergency and crisis) expenses are expenses associated with contingency/emergency planning and crisis management in general.

These expenses usually have a budget to spend from, but they are  (1)  unknown in advance (2) unpredictable in timing and (3) unknown amounts of money involved

This depends on several unknown/unpredictible factors due the nature of the subject of contingency/emergency and crisis management.  ... (1) whether the contingency happens or not  (2) If it happens, how long it lasts (duration), (3) while the contingency exists, what is the extent of the damages/losses (4) What would be involved (expenses) in the recovery from such contingencies .

So, it is may be good practice for organizations to allocate a budget (variable in percentage from their total operational budget) depending on the risk level assessment associated with this business and its environment, circumstances and specifics .. 

Let me give you an example from a5-day course which I taught on the subject of "Crisis Management and Reputation Proection in the Energy sector" 

When the oil spill happend back in the Gulf of Florida in2010,  do you know how much this cost BP ?? and where did this money come from ??  What kind of expenses were involved ? and where the money was spent ??