If your home's electrical service panel (breaker box) is full and you need more room to add new circuits, installing a subpanel might be the way to go. Subpanels certainly can add convenience and plenty of room for installing new circuits, but your current system must have enough capacity to support a subpanel. Alternatively, if you need just one or two additional circuits, you may be able to get by with a tandem breaker or two.
A subpanel is fed by a large double-pole breaker in the main service panel. This means that the main panel must have sufficient capacity to support the additional demand of the subpanel. If you currently have a 200-amp main panel and are using less than half of this capacity, you can probably add a 100-amp subpanel with no trouble. On the other hand, if your current service is 60 amps, there's no way your old main panel can support a subpanel of any suitable size. The solution here is to upgrade the main panel, most likely to a 200-amp panel, before adding a subpanel.
Subpanels must be large enough to justify installing them in the first place. For a large home addition or sizable kitchen redo, remodelers often add a 60-amp subpanel with at least 12 slots for circuit breakers. Subpanels are often larger when they supply (and/or are installed in) a detached garage or a workshop or large office in a separate building from the main house.
In this case, a 100- or 150-amp subpanel might make the most sense. If you're going to the trouble of bringing power out to a separate building, you want to be sure to have enough capacity for the future.
Sizing a subpanel is much like sizing a main service panel. You add up all of the electrical loads in the area the panel will serve, then add 20% or 25% more capacity to provide some flexibility for adding circuits in the future.
Subpanels bring circuit breakers closer to where the power is used. For example, a subpanel in a remote workshop makes it easy to shut off the power or reset breakers right at the workshop, saving you the trip back to the main panel at the house. Subpanels also help with voltage drop, a loss of power over long wiring runs. Voltage drop occurs on all wiring, but the loss is negligible until you get over about 75 feet or so. Increasing wire size reduces voltage drop. Because subpanels are fed by a few large wires, they can bring power to a location far away from the main panel without sacrificing too much to voltage drop. By contrast, running standard circuit wiring from the main panel to a distant location -- and making a separate run for each circuit -- incurs voltage drop and uses a lot more wiring.
If your main panel is full but you need only no more than a few extra circuits, you may be able to get away with using tandem breakers instead. These are special breakers that serve two separate circuits but take up the space of only one breaker in your panel. There are a few catches, though. First, your panel must have the capacity to support the added circuits.
Second, the panel must be designed for tandem breakers. Most newer panels have some slots that are compatible with tandem breakers; if yours does not, you can't use them. Finally, tandem breakers must be legal in your area; check with the local building department for details.