I have been wondering how could aging process differ for a person moving close to velocity of light or for a person close to a very strong gravitational field compared to a person who is in a slow motion. This indicates that molecular reactions happening in our body slows down when you move closer to velocity of light? And if so how is that possible?
Time dilation does not mean slowing down of motion. Only the process as it is observed by an observer (that means the observer's measuring of the moving object) is slowed down. The object itself does not realize any difference on itself while moving. Time is dilated for the observers, the proper time of the object remains constant.
By consequence, from the point of view of the observer (and according to the measurements of the observer), molecular reactions happening in our body slow down when we move closer to velocity of light. This is a phenomenon due to the so-called twin paradox.
A moving frame's x' and t' is different than a x and t of a stations rest frame. A moving frames x' and t' is actually a linear combination of a stationary frame x and t. This is analogous to changing to a rotated coordinate system x',y',z'. Functions need these new variables substituted in after the rotation is performed. So you get thing like x/3, 2z, etc being put in the functions that remain associated with the rest frame. That's why its possible for reactions to slow down as they are moving.