The Interior Ministry is responsible for police, road safety policing, economic/tax crimes investigations, and the Interior troops. The most feared are the OMON, nicknamed "animals" by Russian citizens for their cruel methods used in protecting the government from the people, which is their main duty. The regular police are often nicknamed "bandits" as they are frequently accused of stealing from citizens via corruption.
Separate from the Ministry of the Interior is the Federal Protective Service or ФСО (FSO), responsible for guarding the highest ranking members of government, and is under the direct authority of President Putin and his director of personal security. That organization is more secretive, and has somewhere between 25,000 and 35,000 members, many plainclothes officers with the power to make arrests and conduct surveillance outside the jurisdiction of the courts.
Those high stepping young guards at the Kremlin and outside the Kremlin guarding the Tomb of the Unknown soldiers, the Kremlin Regiment, might have fooled you with their young looks and what at first glance seems like largely ceremonial duties. In reality, they are highly trained members of the FSO, many of them over time will climb up the ladders of the FSO or other security services.
Given Mr Putin's highly sensitive fear of some kind of "colour revolution," it is unlikely that these layoffs trimmed the ranks of those who keep the public in check during times of crisis.
If secretaries and managers are the ones to receive "pink slips," then it will have been a cost cutting move. That is my guess at first glance.
If however, it means that some employees move into the ranks of other security organs, then it might indicate some sort of maneuvering behind the scenes--likely by the FSB to keep a certain president on a short leash. There could be a tug of war going on in the shadows, and some say that the FSB is not happy about the measure of freedom and authority given to certain Republic leaders.