Psychology is the study of mind and behaviour. Develop means to grow and change. So Developmental Psychology is the scientific study of how humans develop from birth to death.
Much of the studies have to do with childhood, since this is when humans change the most rapidly.
For an overview of Developmental Psychology you can check out this video:
Usually a Developmental Psychologist will focus their expertise on one stage of life. Some will examine children and make sure they are developing at a normal rate or when milestones are normally expected. Others may study people who are elderly to help them have a more full, active life.
Nature in Developmental Psychology refers to the human characteristics that are innate or contained within our genes. Things like skin color, personality traits or vulnerability to certain diseases are determined by our make-up.
Nurture addresses the environment that we grow up in and how it affects us; our upbringing, culture and social background.
This question of what influences humans: nature or nurture is an age-old one. Most modern Psychologists feel that both have influence.
For a further discussion of this, check out this source: