Here are the pointers.
The Supreme Court is not elected by representatives of the people. They are elected by other Supreme Court justices as well as from the Israel Bar Association.
The Supreme Court has the ultimate say on any law passed in Israel. They govern purely on "feelings", there is no constitution they base rulings on. This means that if the Knesset passes a bill regardless by what % of MK's voting for the bill. The SC can cancel that law/bill by a simple majority and the knesset cannot do anything about it.
The reform bill basically wants to give the elected officials of the Knesset the ability to choose who should be on the SC just like in the USA. They also want to take away the ability of the SC to cancel basic laws. They want to put the power back in the hands of the knesset who are democratically elected by the people.
This terrifies the left in Israel since they know they will never have a majority again in the Knesset. They will always need to rely on people like Lieberman, who although sat with Lapid is generally Right Wing, Gantz as well is Center Right and will also want more right wing judges if it was up to the Knesset. The left in Israel has only one thing preventing a true right wing country. That is the SC and that is why they are fighting until the bitter end.