A merger in simple words refers to combining of two companies into one. According to differential theory of merger, one reason for a merger is that if the management of a company X is more efficient than the management of the company Y than it is better if company X acquires the company Y and increase the level of the efficiency of the company Y.
According to this theory if some companies are operating at level which is below the optimum potential of the company than it is better if it is taken over by another company. This theory also implies that management of a company is also not efficient in running the company and therefore there are always chances that it will be taken over by other companies.
Differential theory can be particularly helpful when a company decides to take over other company in the same industry because than it would mean that company which is taking over other company can expand without much cost because of the efficient utilization of all the resources. However there is one risk to this, which is if the acquiring company pays too much for acquiring the company, but in reality the resources do not get utilized in a manner which is forecasted than it can lead to problems for acquiring company.