Random walk hypothesis is created as a neo-classical consumption function by Robert E. Hall, and it is related to an expectation theory in macro economics. This gives basis of how individuals do economic decision of present period and is used to calculate an amount of the macro consumption from an economic world.
This theory starts with Freidman's permanent income hypothesis and Lucas's rational expectation hypothesis. Before this theory was made, other expectation theories basically assume that people irrationally think sometimes making decision based on the past (already reflected in the market) facts or falling into the illusion. But Lucas argued that the market players use all the information available at the moment in order to pursuit utility maximization. Permanent income hypothesis supposes people try to decide the amount of consumption expecting the impacts of a certain incident throughout the whole periods of time.
Random walk hypothesis concludes rational expectation to consumption of the next period is the present consumption. It is because all the information was taken into account on the decision of the present consumption. What changes the amount of next period consumption is totally unexpected or not given information. Therefore, the changes in the consumption cannot be expected but randomly walk.