Art, Time, Future, Past and Present are capitalized in the poem because they are personified.

Art is long, and Time is fleeting,

Trust no Future, howe’er pleasant!
Let the dead Past bury its dead!
Act, — act in the living Present!

Art (the work we do) is long-lasting, Time is escaping our hands, Future is not trustworthy, Past is dead and the Present still alive. This is how Longfellow describes them. These are the forces that can rule people’s lives. Our lives differ based on how effectively we use our time to act, whether we trust our bright future and be complacent or be sad thinking of the past failures or utilize the present time. So, these elements may be symbolic of the control we have over our lives.