Independence day in Hebrew is "יום העצמאות". Of course it's big! it's one of the biggest and most fun occasions in the year!
Usually, at the night of the independence day, people go out on the streets, watch concerts and fireworks. The day after we usually have a family "מנגל" (barbecue) which is one of the hallmarks of the holiday.
Interestingly, the day before the independence day is the memorial day for the fallen soldiers and those who were killed by acts of terror. This is in order to commemorate those who gave their lives so we could celebrate the independence day, so you could imagine it's a pretty sharp transformation from sadness to happiness (which is pretty unique).
You can read more: https://en.wikipedia.org/wiki/Independence_Day_(Israel)