As well as dividing the atmosphere up into boxes, time also progresses in finite intervals. In the climateprediction.net model, the basic time step is half an hour. The model starts from a set of initial conditions for the atmosphere and ocean and then calculates what they will have evolved to after half an hour, 1 hour etc.
Choosing the time step is not easy. If you want to run a model through 50 years as quickly as possible, you want to use as large a time step as possible. Unfortunately, this isn’t possible because, with a time step over some critical level, the model becomes unstable and stops working. In very simplified terms, you can think of this as happening when the time step is so large, that air (or, more accurately, energy) can travel further than one grid box in one time step, and it becomes impossible to accurately determine how the fields develop.
However, some things in the atmosphere change more rapidly than others, and so need to be calculated more frequently. So, for example, the dynamics (essentially the movement of the air) needs to be calculated every half hour, but the radiation (the balance of incoming and outgoing energy) can be calculated less frequently. This is why, if you watch the model running, it seems to complete some time steps much more quickly than others.
In the ocean, the ratio of the horizontal grid size to the length of a time step must not exceed the largest flow speed of water in the ocean.