Hamas fighters breached the border from Gaza - a Palestinian territory occupied by the Israeli military.
A spokesperson from the organisation told the BBC their violence is a response to attacks by Jewish settlers.
Israel has responded with fierce counter-attacks.
Prime Minister Benjamin Netanyahu said Israel will take "mighty vengeance for this black day".
Hilla Sebton lives in a kibbutz with her family just 700 metres away from the Erez checkpoint on the Gaza border where ground assaults took place.
She, her husband and three children were told to lock down in their home while the attack raged around them.
Sebton spoke to Ingrid Hipkiss.
