What does it mean to go on a "vision quest" please?

Hello Dtnl42

Thank-you for your question which was an interesting one to research for you.

I will attempt to answer it by providing you with a list of recognised
definitions but in summary a vision quest is a rite of passage
(usually taken by Native American people) to gain knowledge and
clarity.  Therefore to "go on a vision quest" would normally refer to
someone embarking on a mission to find or gain knowledge (possibly
starting new research on a subject).  A "vision quest" usually refers
to achieving spiritual healing but in a modern day context can mean to
gain any knowledge.

"Vision quest: A period of spiritual seeking among certain Native
American peoples, often undertaken as a puberty rite, that typically
involves isolation, fasting, and the inducement of a trance state for
the purpose of attaining guidance or knowledge from supernatural
forces."
http://dictionary.reference.com/search?r=2&q=%20vision%20quest%20

"Vision Quest: A ceremonial process usually experienced in and with
nature and with a guide of mastery, by which one seeks a vision into
the unknown to gaze into the mystery for purpose, direction and
clarity."
http://www.align.org/glossary.htm

"Vision quest: An attempt to envision and communicate with a
supernatural being, commonly undertaken by Illinois Indians at the age
of adolescence."
http://www.museum.state.il.us/muslink/nat_amer/post/htmls/gloss.html

"VISION QUEST: Native American tradition and old native culture?s rite
of passage. A call for a period of time to be alone with nature."
http://www.sabrinasdayspa.com/topics/glossary01.htm

"Vision quest: A rite in which a young person or young adult goes to 
an isolated place to seek, in a vision, a protective spirit."
http://thedesmonds.com/glossary.html

"A vision quest is a quest for the visions in anyone?s life that will
heal them and make them whole. In traditional first nations cultures
young people were sent into nature to listen to the voices of the
living earth. The elders taught them to do this to find their path in
life and to find their power animal helpers. The person on the vision
quest spent days in caves, on mountain tops, on rivers, in the desert,
waiting, and inviting the voices to come to them. When they heard the
voices and saw their vision, they would return to their people and
know who they were and what they were to do. This book will be about
how to evoke a similar experience for you in our own contemporary
culture."
http://www.pathofthefeather.com/pof3.htm

Other useful links:
http://www.crystalinks.com/visionquest.html

If you have any questions regarding this answer please ask for
clarification and I will do my best to help.