Within the storm waves of different size, power and shape are generated and the longer they are subject to the wind the more energy they contain. This is called windsea, it describes waves still subject to the winds that created them.
In time most of the waves in a windsea will travel away from the winds that created them. Once this starts to occur they're on their way to becoming 'swell'. The tiny initial capillary waves created by the wind die quickly simply because of the surface tension of the water, but the larger waves are constrained only by gravity and, left unimpeded, can travel many thousands of miles from the storm that creates them.
In fact the forces decaying waves are so small in action that the main reason that the more powerful longer period waves decay as they head away is a simple concept known as circumferential dispersion. If you can imagine a wave travelling like ripples in a pond once you've thrown in a stone you can imagine a small circle growing ever larger as it spreads away from it's source. Now once the wave has left the storm there's no energy being added, so as the circle grows the waves energy is spread over an ever larger circle. This means that at any point on the circle as it increases the wave height will decline. The relationship between wave energy and height is such that for every doubling of the distance a wave travels from the storm the height will decay by about 15-30 percent. Waves generated by powerful storms can travel many thousands of miles from their origin before they finally hit land. Waves can be generated in the South Pacific and create surf on Alaskan beaches.
As waves travel from a storm something very important to us as surfers starts to happen. We've mentioned that there's a direct relationship between wave period and how fast a wave travels. We've also mentioned the mix of wave heights and periods created during a storm. So putting the two together we can start to understand that as the waves move away from the storm some will travel faster than others. Now if you're surfing on a beach relatively close to the storm you won't notice too much effect from this, the different waves from the storm will all arrive at about the same time. You'll surf in this same jumble of sizes and periods that was originally created. The sea will look somewhat 'confused' or 'messy'. If, however, you're lucky enough to be surfing in waves that have travelled some distance from the storm that created them you'll be surfing in much more consistent conditions. For you the arrival of a new swell will look something like this: