what means Probablity of event excedence of so many years

I think this is the annual flood chart. The USGS earthquake hazard and probability maps are colored and have contour lines.

Exceedance probability in Y years. (This part is mathematical)

The expected number, n of exceedances in Y years is n = Y times r, the annual rate of exceedance. Assumption: The rate of earthquake occurrence in time is governed by the Poisson Law. Application: Under the Poisson Law, if you expect over some period of time n occurrences of “something”, the probability of 0 occurrences is e–n. If the “something” is exceedance of some ground motion, the probability of getting an exceedance is 1 – P(0). So, one can work backwards to find the annual rate of exceedance corresponding to “the probability of exceedance is 5% in 50 years.”

Quote from USGS, learn basics. USGS link.

Probability of Event Exceedance of a certain period of years, lets say within N years; is the probability of occurrence of the X-year-flood event, in which the peak flow the gained from statistic for a certain country or area, will be exceeded.

Which in this case is flooding. And the Annual maximum daily flow was recorded in that particular year of occurrence, it served as a basic for calculating the probability of the event occurrence in the future period of N year.

In the topic of civil engineering particularly, as we discuss, we may have to refer to the past data to justify the design limit states for a certain project or building.

Say for a housing estate construction, we calculated the surface runoff into the lower region displaced by the construction of the housing estate (concrete, roads, etc). Then in designing the diverting drainage, we have to justify what is the size required to contain the flow rate of the runoff.

Depending on what type of the projects, we may need to include the probability for exceedance for a certain year. Say 100 years for residence building, or 1000 years for a dam.

Anyhow, the statistic itself does not justify the design, but an engineer who do the design. For an instance, he or she may have to include that the possibility of climate change would drastically increase the maximum flow, then design it differently rather than just following the data blindly.