What is the goal of Meditation- is it increasing the gap? When I sit for meditation, sometimes I realize my breath has stopped and thoughts are subtle, for but a very minimum amount of time, but that time I feel totally in a present moment, in a moment. 

It this a goal of meditation? or something else? or analyzing? When is the awareness aware of awareness? Is feeling the gap awareness?
Source: Anapanasati

If you see step 4 above it says "Tranquilise the bodily activities". In this stage you do calm the breath, i.e., increase the gap, but you do not manipulate the breath directly. 

For further reference on claiming the breath see: LECTURE THREE: CALMING THE KAYA from ANAPANASATI - MINDFULNESS WITH BREATHING Unveiling the Secrets of Life: a Manual for Serious Beginners by BUDDHADASA BHIKKHU, Knowing and Seeing 4th Ed. by Ven. Pa-Auk Sayadaw p35.

Also in meditation you have to be in the present moment and see arising and passing or sensation at the present moment as you have realise.