Providing a good weather forecast is a difficult task. Nowadays every serious forecast is based on computer simulations. The method of using computers for the forecast is called numerical weather prediction (NWP). The atmosphere is divided into a 3-dimensional grid, so that the computer can use it. Every grid point has individual values of the common meteorological variables as pressure, temperature, winds and further more. The prediction makes use of many physical laws. Through mathematical formulations these physical laws are adapted to be usable on the numerical grid. As the equations include the time as a variable, the computer can calculate the state for a time point in the future!
Everybody can imagine, that the copy of the atmosphere is more accurate if the numerical grid is finer, because it is more similar to the real atmosphere. Due to this fact the quality of weather prediction depends strongly on the resolution of the numerical grid, that is used. The crucial point is, that the finer my grid the larger is the calculation of my computer. Let us say that we double the resolution of our grid. Then - because the numerical grid is 3-dimensional - our computer has to calculate just about eight times as much! Therefore the quality of the weather forecast strongly depends on the performance of the used computer, because the computer has to perform the simulations of our weather predictions.
A good and reliable weather forecast is usually limited to about 5 days. Every longer forecast typically provides no gain of information.