There are two different wind events that are most common around Western Washington. There's a pattern that brings strong easterly winds to the Cascade foothills, and another that brings strong winds to the Western Washington lowlands.
Lowland Wind Events
Wind is created from a difference in pressure. The atmosphere is always trying to maintain an even pressure, so air will blow away from a high pressure and toward lower pressure. The Earth's rotation, atmospheric friction, and mountainous terrain all have affect on that process.
In the fall and wintertime, many storms will tend to make landfall across the southern tip of Vancouver Island or the northern tip of Washington state.
When we get our strongest wind events in the Puget Sound and other lowland areas, it's usually due to a strong center of low pressure moving by just to our north.
As the storm approaches the Northwest coast and Vancouver Island, the coast and "Northwest Interior" (basically Everett north to the Canadian border, and west to Port Townsend, including Camano, Whidbey and San Juan Islands) will get strong south to southeast winds as air rushes out toward the center of the storm.
Interestingly enough, the central Puget Sound area still stays somewhat wind sheltered at this time because the Olympic Mountains block a direct wind path to the low.
However, as the storm tracks inland and crosses the area due north of the I-5 corridor (think of an imaginary line of Interstate 5 extending north forever), you now have a direct wind path to the low in the Puget Sound area, and a very strong difference in pressure -- very low pressure north, and relatively higher pressure to the south.
Air will race north through the I-5 corridor to meet up and try to fill the lower pressure to the south. As the air gets "squeezed" by the mountains on both sides of Puget Sound, the air will accelerate (this is called the "Venturi Effect", if you're curious.)
Think about blowing through straws. If you have a large straw, the air coming out the other end is moving somewhat slow. But if you then apply the same pressure through a smaller straw, the air coming out the other end is moving much faster. The mountains act as if they're shrinking the straw.
The speed of the winds depends on a variety of factors. The strength of the storm, the track of the storm, and how strong the higher pressure is to the south all contribute to how fast the winds will blow. A stronger storm that comes inland further north may produce the same winds as a weaker storm that comes in closer to Seattle.
Cascade Wind Storms
The areas of Enumclaw, Gold Bar, North Bend, and Cumberland have their own wind machines. The physics is similar, but the setup is a bit different.
There, we need strong high pressure in Eastern Washington and lower pressure in Western Washington. The best setup is when a strong storm is located due west of the Washington Coast.
Now, you have wind racing west to meet the lower pressure offshore. But the Cascades make a formidable barrier. Thus, the wind has to sneak through whatever cracks it can find in the terrain -- mainly Cascade Passes.
But there, you have very narrow passageways, so the wind speed accelerates. Thus, places at the outflow of the passes can see very strong winds. Cumberland has the unique situation of being at the end of a very narrow valley, which works like their own private wind tunnel.
All Together Now!
Frequently, you'll have a pattern where a strong storm is approaching Washington from the southwest. As the storm passes due west of Washington, strong east winds will pick up along the eastern foothills.
As the storm begins to move to the northwest of the state, the Cascade winds decrease as the winds become more southeast, but now the southeast winds pick up along the Coast and North Interior.
Finally, as the storm moves inland and due north of Seattle/Bellingham, the south winds pick up through the Puget Sound area. Meanwhile south to southwest winds continue to blow along the Coast.
Winds then gradually decrease as the storm moves away further east.