Israel is a parliamentary democracy.
A "unity government" or a "national coalition government" is a special type of coalition government formed with the support of most of the major political parties represented in the Parliament. The motivating force for creating such a coalition government is often some national crisis or unique political situation in a country where a need is felt to project political solidarity to the public.
One such famous government was "Churchill's War Coalition" in the United Kingdom, during World War 2:
Two out of five members of Churchill's 1940 War Cabinet were Labour politicians, one was National and two were Conservatives. Domestic political fighting was put on hold and all three parties worked together with the common aim of defeating Nazi Germany.
When the opposition joins such a coalition government, and agrees to a set of common political goals to resolve the political crisis, the coalition government attains a kind of "super majority" in the Parliament. Thus, during war time or some other political crisis, such a government can respond and act more quickly, without the legislature holding it back.
Another advantage of such a national, coalition "unity government" is that it allows the political blame for any failures to be shared among all the parties in the coalition. (This gives the government more latitude to take publicly unpopular decisions, if necessary).
The heads of two opposition parties said Sunday they were open to the idea of temporarily joining an emergency unity government headed by Prime Minister Benjamin Netanyahu ... National Unity party leader and former defense minister Benny Gantz said he was willing to join the government on condition that his party be given real influence in directing the war against the Palestinian terror group in Gaza.
In the negotiations for the formation of the current unity government in Israel, the opposition leaders are reported to have made the following demands:
Gantz has been insisting on the formation of a small war cabinet with “real influence” over the management of the war, expected to include at least two opposition politicians with the highest levels of military experience. Both Gantz and fellow National Unity party member Gadi Eisenkot are former Israel Defense Forces chiefs of staff, and Gantz is also a former defense minister.
... The war cabinet is meant to supersede the broader security cabinet, which includes far-right party heads widely considered to be complicating Israel’s security policy vis-à-vis the Palestinians, causing Netanyahu to largely circumvent it thus far during the war.
... Opposition Leader Yair Lapid also offered to join an emergency unity government, but preconditioned his offer on sidelining “extremists.” While he did not call them out by name, Lapid was understood to have meant National Security Minister Itamar Ben Gvir and Finance Minister Bezalel Smotrich.
... Liberman, also a former defense minister and a Netanyahu ally-turned-rival, offered to join the government with the precondition of a commitment to destroy Hamas’s presence in Gaza, but was not included in the talks even though the coalition is understood to support the demand in principle.
Most of these demands were acquiesced to, and a unity government was successfully formed.
An agreement is reached to bring Benny Gantz’s opposition National Unity party into an emergency government amid the war with Hamas in Gaza following days of negotiations, Prime Minister Benjamin Netanyahu and Gantz announced in a joint statement.
A small war cabinet to direct the war with Hamas will be created, as demanded by Gantz, which will include just Netanyahu, Defense Minister Yoav Gallant, and Gantz ... For the duration of the war, five members of the National Unity party will be added to the broader security cabinet which operates under every government — Gantz, Eisenkot, MK Gideon Sa’ar and two others yet to be determined.
No legislation in Knesset or government resolutions will be advanced during the war that are not related to managing the war, it was agreed.
Due to Israel's political history, such "unity government" are now part of Israel's political culture - from 1967 onwards Israel has had more than 6 such national "unity governments". Thus, the Israeli public also has an expectation for a "unity government" during times of extreme crisis.
(On a side note, even Fatah and Hamas have once considered forming a "Palestinian Unity Government").
Unity Coalition Governments: Explainer
Winston Churchill 1940
Gantz, Liberman open to emergency unity government, but demand say in waging war
Gantz, Netanyahu close in on emergency unity government, 5 days into war
Netanyahu, Gantz agree to form emergency unity government
Israel's National Unity Governments: A Retrospective