Here's the first definition that appeared when I Googled "stochastic":
adjective: stochastic: randomly determined; having a random probability distribution or pattern that may be analyzed statistically but may not be predicted precisely.
According to Wikipedia, "In probability theory, a purely stochastic system is one whose state is non-deterministic (i.e., "random") so that the subsequent state of the system is determined probabilistically. Any system or process that must be analyzed using probability theory is stochastic at least in part. Stochastic systems and processes play a fundamental role in mathematical models of phenomena in many fields of science, engineering, and economics.
Stochastic comes from the Greek word στόχος, which means "aim". It also denotes a target stick; the pattern of arrows around a target stick stuck in a hillside is representative of what is stochastic.
In other words, "stochastic" means "random." Here's an image used to illustrate a course called "Stochastic Processes," taught in the Electrical and Computer Engineering Department at Utah State University in 2006.
Another image that could illustrate "stochastic" might be the pattern of clothes thrown in the general direction of the dirty clothes hamper when my home was occupied by several people with not the greatest aim.
Unfortunately, I can't find a photo of that on the Inter Web. However, I just made my very own photo of that, with my very own pile of socks and my very own dirty clothes hamper:
|Stochastic scattering of socks thrown in the general direction of the hamper (Or is this a better illustration of entropy?)|