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.”