What influences the moderate weather in Dublin?

Dublin sees somewhat abrupt changes in weather—one day being cool and dry and the next being cold and wet—due to the fact that it lies underneath a convergence zone of cold air, warm dry air, and warm wet air.

http://www.met.ie/climate-ireland/climate-of-ireland.asp
As you can see in the image above, Ireland location—“50º and 60º north of the Equator and around 15º south of the Arctic Circle” —places in the middle of five different streams of air flow, and since it is an island the effects are greater due to the surrounding oceans
and its smaller land mass.

Dublin’s close proximity to both the Irish Sea and the Atlantic Ocean play a significant role in the moderate maritime climate that this beautiful region of Ireland sees. Ireland is affected mainly by air coming from the North Atlantic drift—the eastern extension of the Gulf Stream, but it affects the areas bordering the Atlantic coast line more so then the areas within the continent as the mountains and cliffs along the coast act as a shield from the winds. Due to the close proximity of the North Atlantic drift in winter, Ireland tends to a have more windy and cool climate than in the summer when the drift reaches farther North.
The weather in Ireland can at time shift abruptly if the polar front shifts in position—the polar front acts as transition zone for cold, dry air which is moving southwards and warm, wet air which is moving northwards.

http://www.met.ie/climate-ireland/climate-of-ireland.asp
In this image, we see one of the other major factors in Dublin’s moderate climate, the Polar front.
If you look at when the purple line circles around the L in upper right, you will see the red line of
warm air moving north converge with the blue line of cold air moving south.

Dublin located on the eastern coast experiences some of the driest weather in Ireland due in part to its distance from the Atlantic Ocean and the fact that most of the air Dublin receives comes from the Polar Continental flow—which is cold, dry air—and the Tropical Continental flow—which is warm/hot, dry air.

Seasonal Average Mean Sea Level Pressure
http://www.met.ie/climate-ireland/pressure.asp
In the image above, you can see how the pressure is lower in winter and autumn as the isobars are closer together
and in summer and spring the isobars spread out as the pressure tends to be higher during these seasons.

http://www.weather-forecast.com/static_maps/Ireland/wind/12
In this image, you can see the air/ surface winds coming up from the south—the warm, wet
tropical maritime air—moving along the western coast of Ireland and only a small amount
making in it east towards the Irish Sea and Dublin.

http://www.weather-forecast.com/static_maps/Ireland/cloud/12

In this image, you can see that most of the clouds lie over the Atlantic Ocean and southwest or northeast from Dublin.