What is botanical medicine [3]? Simply put, they are plants (or substances that come from plants) that are used to treat or prevent disease. Plants have been used in this way in all cultures from pre-history on.
Many people use the term herbal remedies, which is fine. We call them botanicals because, technically, the term botanical medicine is more inclusive and includes plant parts that are not strictly herbs, such as bark, seeds, roots, and stems.
Dietary supplement is a government category that determines how substances are sold and regulated. Some fast facts:

Have you ever wondered if a botanical really works? Or if there were any risks in taking it? Or even if the brand you are taking is good? These are all great questions that deserve answers.
Research shows that many botanical medicines offer health benefits, often without some of the risks or side effects of pharmaceutical drugs. However:
In short, learning about botanical medicines can help you get the most benefit while reducing the risks.
You are not alone in your interests in botanical medicines. In the U.S., botanical medicines are one of the most popular and rapidly growing of all complementary therapies. In 2010, the global retail sale of botanical dietary supplements amounted to more than $25 billion, according to Nutraceuticals World. With this buying power, the more the American public knows about botanicals, the more it can influence good government regulations and reward manufacturers who produce quality products.
Blumenthal, Mark, Ferrier, Grant, K.L., Cavaliere, Courtney (2006). Total sales of herbal supplements in United States show steady growth. Herbalgram, 71, 64-66.
Dennis, J. Dietary Supplements 2010. Nutraceuticals World. April 1, 2010.
Dietary Supplement Health and Education Act [5] of 1994
Morris, C.A. (2003). Internet Marketing of Herbal Products. JAMA, 290:1505-1509.
Links:
[1] http://takingcharge.csh.umn.edu/sites/default/files/files/images/xBotanical med theme.jpg
[2] http://takingcharge.csh.umn.edu/sites/default/files/xBotanical med theme.jpg
[3] http://takingcharge.csh.umn.edu/glossary/3#term8
[4] http://takingcharge.csh.umn.edu/botanical-medicine/are-botanical-medicines-safe-0
[5] http://www.health.gov/dietsupp/ch1.htm
[6] http://takingcharge.csh.umn.edu/our-experts/dennis-mckenna-phd
[7] http://takingcharge.csh.umn.edu/activities/what-botanical-should-i-use
[8] http://takingcharge.csh.umn.edu/activities/interactive-history-botanicals
[9] http://takingcharge.csh.umn.edu/activities/making-botanical-decision