In my old age you may see

Me holding on to life

My body is getting older and colder

His old body is slow, he is at peace

Meaning: 

He is comparing his old age and him dying soon to a fall tree.

In me you see the my old age

As the sun sets in the west

The night takes away one more day of his life

The night brings him closer to rest.

Meaning:

When the sun sets and it becomes night, it is referring to him having one less day to live. "Death's second self" is a reference to the night and how it is taking his life away.

In me you see my strength

My young life lies

On my deathbed where they die

Consumed in happiness

Meaning:

His memories are dying because this is his time to die. His fire is his youth and it nourshied his when he was younger.

By us understanding death, it makes our lover stronger

To love someone that much you have to leave them behind

Meaning:

This couplet gives the speaker relief and understanding that death is not a bad thing.

Commentary/criticism:

http://shakespeare-online.com/sonnets/73detail.html

(scroll down to sonnet 73)