What, according to the poem "A Psalm of Life," is our ''destined end'' or purpose?

According to Longfellow's poem, our "destined end" is:

to act, that each to-morrow
Find us farther than to-day.

This means that, rather than worry about whether we are enjoying ourselves or feeling sad, we should focus every day on what we can accomplish in the here and now, so that by tomorrow the world, even in a small way, is improved.
This is a poem about action: it is telling us we need to act in the present moment. Time is "fleeting" says the speaker, which means it is moving very fast. We don't have time to waste dwelling on the past or thinking about tomorrow: we need to "Act,— act in the living Present!"
If we do this, we can possibly leave our "footprints in the sands of time." These footprints are the memories others hold of what we have accomplished after we are gone. We need to put our heart into whatever we are doing and work hard at it so that we can have a lasting impact on the earth.