What is the meaning of Allaahs name al-Hayiy?

The
Prophet (peace and blessings of
Allaah be upon him) described his Lord as being modest. The modesty
of Allaah cannot be comprehended by human understanding, and no mind
can understand its nature. It is modesty that is based on kindness,
goodness, generosity and majesty. By His mercy, generosity, perfection
and forbearance, Allaah is too modest to expose His slaves, show them
up or carry out His punishment on them. He is too modest to reject anyone
who stretches forth his hand to Him, and He loves people who are modest.

 Ibn
al-Qayyim said:

 “He
is the Modest who does not expose His slave even though he audaciously
commits sin.

But
He covers him, for He is the Concealer, the One Who forgives.”