The normal climate condition for a given region is defined with regard to a reference period of about 30 years. So, it's regionally dependent because the normal values of the climate parameters (rainfall, temperature) are determined through a statistical analysis of the times series recorded in the region.
30-year climate normals are the common standard. However, a 30-year averaging period is not necessarily always optimal - especially in light of evidence that climate statistics are not stationary in time. Much has been written regarding the history of 30-year climatic normals, the 'predictive' performance of different normal, and the limitations of long term normals under conditions of secular climate trends. Three documents that one might read (along with references therein) to gain additional background information on the topic are:
(1) Arguez and Vose (2011) doi: http://dx.doi.org/10.1175/2010BAMS2955.1
(2) Huang, van den Dool, and Barnston (1996): doi: http://dx.doi.org/10.1175/1520-0442(1996)0092.0.CO;2
(3) Trewin, B (2007) http://www.wmo.int/datastat/documents/WCDMPNo61_1.pdf
The 30-year normal is recommended by the World Meteorological Organization (WMO). The latest 30-yr period is 1981-2010. Averages of climatic variables over the period are regarded as normal climate, and any departures from the normal are regarded as anomalies.
it is difficult to say what is 'normal'. Even if we restrict ourselves to purely statistical features (average over the past 30 years) we have just the average and this might be a situation that has never existed in reality. The averages consist of maxima and minima; the climate of a place includes these variabilities.