Explain meaning “But a government in which the majority rule in all cases cannot be based on justice, even as far as men understand it”

What this statement refers to is something that Alexis de
Tocqueville called the "tyranny of the majority." Although the idea was not new with him (it is a
major idea in Federalist 10) we use his name for it. The basic idea here is that, if you give the
majority unlimited powers, they can at times use those powers to oppress minorities. This is why
we have a system with checks and balances and a limited government with written limits on its
power (the Bill of Rights, for example).

You can think of examples
from our history where majority rule has abused the rights of minorities. There was the
segregation era when the majority was allowed to deny blacks their rights. There was the time of
McCarthyism when the majority denied the rights of speech and association to those who held the
wrong beliefs. There are other examples in our history.

So, the
basic idea of this quote is that the majority can use its power to abuse minorities if there are
no checks on what it can do. In order to combat this tendency, our system has constitutional
guarantees of rights and a judicial system that has the power to override majority opinion when
the majority is violating those guarantees. (Of course, as mentioned above, even this doesn't
always work to protect us from the tyranny of the majority.)