The term Navagraha denotes the nine celestial bodies which are central to astrological calculations (and beliefs) (and not the nine planets as it is frequently erroneously translated). The Sun, Moon, Mars, Mercury, Jupiter, Venus, Saturn and the two shadow planets Rahu and Ketu constitute the Navagraha.
The nine "grahas" or planets in our horoscope control our karma, our desires and their outcomes. Each of these nine planets exerts an influence in our lives, which is called "dasa" and it can be known from one's horoscope. Navagraha Puja/homam is performed to reduce the negative effects and improve the positive energies related to a person.

Significance
The Navagraha play a vital role in deciding the course of our lives. If 4 or more of the planets are not well placed in ones natal chart, Navagraha homam should be performed.It is also performed if Rahu (Ascending node) and Ketu (Descending node) are afflicted. Navagraha homam is performed if one has kalathra dosha or kala sarpha dosha.The dosha should be nullified to improve marital life and career.
Every graha/planet has its own importance.

Sun is the king of planets which gives health. 
Moon is the planet which rules over mind and gives success. 
Mars or Mangal is the planet which gives prosperity and wealth.
Mercury is the planet which gives knowledge. 
Jupiter gives education 
Venus gives the knowledge of art, music etc. 
Saturn gives happiness and also teaches vairagya. 
Rahu makes life stronger. 
Ketu ensures prosperity in the family.