What happens to the electrical grid when I turn on a heavy load?
When the new load comes onto the grid, a large load current will flow through it.

This load current has to be sourced by the generators. The increased current in the generators throws an increased torque requirement onto the engine or turbine that's driving the generators.

As the engine control at that instant has no way of knowing that more torque is needed, then the turbine+generator combo will start to slow down. The increased output power is delivered from the fall in kinetic energy of the large rotating mass. It's this energy stored in the rotating machinery that is the buffer that allows the grid to handle unplanned load variations.

Spread out over the grid, there is a lot of rotating machinery, so not much change in speed is required to source the power. However, the grid is not infinitely stiff, so the machines local to the load will slow down more quickly. This creates a phase shift between the local machines and the remote grid, which creates a power flow into the local grid area. This distributes the load across the grid, and maintains phase synchronization between the local and remote areas. 

The interconnects between parts of the grid have to be big enough to handle these transient power flows without overloading. For a really big power requirement, say a generating station suddenly goes offline, then the interconnect can drop out, leading to cascading blackouts.

Eventually the engine or turbine controllers will detect the fall in speed, and increase fuel or water flow to match the output power required. The grid controllers will use the instantaneous grid frequency as a proxy for its relative loading, and bring other sources of power online if the frequency is too low.

Over the course of 24 hours, most grids will control the frequency so that there will have been 24 * 3600 * grid_frequency cycles, so that motor-driven electric clocks keep good time from day to day. During the course of a day however, their hour to hour timekeeping could be out due to the load-related frequency variations.