It is known as allelopathy which refers to the chemical inhibition of one species by another.  The "inhibitory" chemical is released into the environment where it affects the development and growth of neighboring plants.  Allelopathic chemicals can be present in any part of the plant.  It can be found in leaves, flowers, roots, fruits, or stems.  The allelopathic chemicals can also be found in the surrounding soil.  Target species are affected by these toxins in many different ways.  The toxic chemicals may inhibit shoot/root growth, they may inhibit nutrient uptake, or they may attack a naturally occurring dependent  relationship thereby destroying the plant's usable source of a nutrient.
 
Do all plants possess allelopathic tendencies?  No.  Some, though they exhibit these tendencies, may actually be displaying aggressive competition of a non-chemical form.  Generally speaking, if it is of a chemical nature, then the plant is considered allelopathic. 

A bit of historical trivia, the 'father of Botany', Theophrastus (ca. 300 B.C.E) wrote of how chickpea 'exhausts' the soil and destroys weeds.  In 1 C.E., it was written how chickpea and barley scorch up corn-land.  It was also mentioned that Walnut trees are toxic to other plants.
 
Allelopathy is a form of chemical competition in that plants are competing through 'interference' chemicals.  By  definition, competition assumes one of two forms, exploitation or interference.

Competition is used by both plants and animals to assure a place in nature.  Plants will compete for sunlight, water and nutrients and, like animals, for territory.  Competition, like parasitism, disease, and predation, influences distribution and amount of organisms in an ecosystem.  The interactions of ecosystems define an environment.

 When organisms compete with one another, they create a condition of resource limitations and possible extinctions.  Allelopathic plants prevent other plants from using the available resources and thus influence the evolution and distribution of other species.  One might say that allelopathic plants control the environments in which they live.
Let us examine the chemical warfare that could be taking place in your garden.
One of the most famous allelopathic plants is Black Walnut (Juglans nigra).  The chemical responsible for the toxicity in Black Walnut is Juglone which is a respiration inhibitor.  Solanaceous plants, such as tomato, pepper, and eggplant, are especially susceptible to Juglone.  These plants, when exposed to the allelotoxin, exhibit symptoms such as wilting, chlorosis (foliar yellowing), and eventually death.  Other plants may also exhibit varying degrees of susceptibility and some have no noticeable effects at all.  Some plants that have been observed to be tolerant of Juglone include lima bean, beets, carrot, corn, cherry, black raspberry, catalpa, Virginia creeper, violets, and many others.

 The Tree-Of-Heaven, or Ailanthus (Ailanthus altissima) is a recent addition to the list of allelopathic trees.  Ailanthone, an allelotoxin extracted from the root bark of Ailanthus, is known for its "potent post-emergence herbicidal activity".  Ailanthus poses a serious weed problem in urban areas.
 
The major constituent of sorghum that causes allelopathic activity is sorgolene.which is found in the root exudates of most sorghum species and has been shown to be a very potent allelotoxin that disrupts mitochondrial functions and inhibits photosynthesis.  It is being researched extensively as a weed suppressant.
 Always remember, if you are not sure if the plant you are getting is allelopathic, ask the experts at your nursery either local or online such as Tnnursery.net.