Yes, we definitely do believe we have a purpose in life.  
 
In a short definition, We believe we are on Earth so that we can become more like our Heavenly Father. We are here to experience life-- the good part and the hard parts, so that we can learn and grow. 
 
to learn more in detail go to these places: 
 
http://www.lds.org/ldsorg/v/index.jsp?locale=0&sourceId=45af9daac5d98010VgnVCM1000004d82620a____&vgnextoid=bbd508f54922d010VgnVCM1000004d82620aRCRD  
(in the above link, make sure you click on "Additional Information) 
 
http://lds.about.com/library/weekly/aaplanofsalvation.htm

If you feel like you do not have a purpose, it is because Satan tries to make us feel like we are worthless and are going nowhere. In reality, we believe each individual has a significant purpose in this life, which is personal to them. So when it comes to personal details, I cannot give you your exact purpose, just the general points for all of mankind. One way an individual can find out these personal significant purposes is by getting what we call a "Patriarchal Blessing," which is a special Priesthood Blessing given by a Patriarch. 
I've gotten mine, and have heard my siblings get theirs, and I can reassure that we each have a special purpose here.