Israel celebrates its Day of Independence (in Hebrew "Yom Ha-Atzma'ut") on the fifth day of the month of Iyar (the tenth month of the Jewish calendar). This usually turns out to be in mid-spring, more-or-less. On this date, in 1948, the state of Israel proclaimed its independence, after the rather sudden end of the British mandate in Palestine.
Independence Day is one of the few "secular" holidays in the modern Israeli calendar. It's also recognised by (mainstream) orthodox Judaism as a day of religious significance (with appropriate prayers to be said), but by and large it's a day of national celebration. The day immediately before it is Israel's Memorial Day, dedicated to remembering Israel's fallen soldiers (and victims of terrorism). The juxtaposition is symbolic.
On the formal side, the Day of Independence starts at Mount Herzl (in Jerusalem, where a very standardised semi-military evening ceremony -- which melds formation marching with some singing and dancing -- signals the end of mourning and the start of the day's celebrations (from evening to evening, as all Jewish holidays). The highlight is the lighting of 12 beacons (one for each of the Bible's twelve tribes of Israel) by 12 Israelis carefully picked to represent some valued ideal or notion. The whole affair ends with fireworks, which are later duplicated at other sites around Jerusalem, and the whole country. Other formal occasions include the Israel Prize being awarded to worthy Israelis at the Knesset, the World Bible Quiz, and distinguished soldiers receiving commendations from the President and Chief of Staff.
Informal celebrations start in the evening, as the Mount Herzl ceremony draws to a close. Outdoor "entertainment stages" in city squares, where Hebrew songs prevail, are popular, and usually draw large crowds. Little flags are common. For no apparent reason, so are squeaky plastic hammers which squeak when they connect with people's heads (and they do!). Also ubiquitous are the misnamed snow spray cans; these squirt long streams of icky white goo, either into the air (which is forgiveable), or all over innocent bystanders' clothes and face (which is a pain). Buildings are adorned with national flags of all sizes, and many cars sprout small fluttering flags, which break or fall off during the next few weeks, and end up rather trampled and miserable along the highways and byways of Israel.
More conventional family or all-night-long club parties are also standard for the evening kick-off, but the real mainstay of Independence Day celebrations is during the day, when families and friends spill out onto every park, beach, and empty lot to barbecue. The mangal (barbecue) is always a popular way to picnic in Israel, but on this one day it's a national craze. A week-long advertising blitz urges Israelis to buy one brand or another of hamburgers, kebabs, shipudim (chicken or turkey on skewers), sausages, or packaged steaks, all of which will eventually end up on the grill. The entire activity is referred to as "fanning"; to get the barbecue coals really hot, the cook will usually be found fanning some air past them with a bit of card, or whatever. The meat is accompanied, by tradition as powerful as law, by hummus, lots of pitas, pickled cucmbers, and some salads (mostly eggplant spread, coleslaw, red cabbage salad, and the everpresent Israeli Salad of tomatoes and cucmbers). The barbecueing Israelis fill every open space, and the traffic jams in some favourite spots are nightmarish. But hey, it's our party, and we'll fan if we want to.