A somewhat abstract term, random walk in finance is commonly used to describe the movement of share prices. Share prices are said to follow a random walk which can be represented by what is called Brownian motion, a scientific term commonly referred to when describing atomic movements.

[https://en.wikipedia.org/wiki/Brownian_motion]

In short, random walk says that shares take a random and unpredictable path. The chance of a shares future price going up is the same as it going down

Share prices take on similar movements in that they are ‘random’, and this essentially forms the foundation of option pricing models through the modeling of share price movements. Options are derivative contracts that give the holder the right, but not the obligation, to buy or sell the underlying financial instrument at a specified price on or before a specified future date.