The Israeli weather generally divided for two seasons the winter and the summer.
Winter in Israel starts in October-November and ends in March. For most Western Europeans, the winter will not look too serious with temperatures in Tel Aviv that can move in average between 17-22 C in the day and 10-15 at night (most days and nights - of course - sometimes it gets colder than this). It rains here and there but sunny days are not a rare thing in Israeli winter. In the northern part of Israel (Galil and Golan) it gets colder than that - some mountain peaks also get some minimal snow in winter. Jerusalem also gets quite cold during the winter and usually gets a day or two of snowfall every year.
April-May is regarded as spring, going into the Summer which is June to September. It should be noted that "spring" in Israel isn't like spring in, say, Europe - this is when the weather is at its most unpredictable. Spring is usually characterized by heat waves followed by suddenly cold weather or even storms. In terms of weather, April can be hit-or-miss for travelers.
May and June are wonderful for travelling with the best weather and just before the summer vacation and very hot days of July-August. The summer itself can get very hot and humid near the seashore with normal temperatures of 28-32 C by day with 80% humidity. In the hills and mountains the summer is calmer and less humid.