The Tjörnes fracture zone in Northern Iceland is showing large amounts of quakes in a swarm that has been ongoing for several days now. Many of the quakes are above 3.0 in magnitude, and are at shallow depth. The area, much like the rest of Iceland, is a spreading/transform fault assembly on the Mid-Atlantic ridge. These quakes could be both tectonic and volcanic in nature, although at the moment no eruptive activity is reported, however it is possible that submarine activity is occurring.
Image from Iceland Meteorological Office
The swarms are occurring near the small island of Grimsney, and the surrounding areas. The largest events, a magnitude 5.3 and 4.7 quake, show up on USGS sensors. Hundreds if not thousands of quakes have occurred within the last few days.
This is a frequent event for this seismic zone. Any eruptive activity, if any, would likely be submarine and not pose a threat to islanders, or the rest of Europe, but Iceland does have a history of creating new land when it wants to as we learned from the 1963-1967 eruption of Surtsey (part of the Vestmannaeyjar volcanic system), which grew a new island out of the ocean during a submarine eruption.
This is unlikely at this point, but if anything further takes place aside from the shaking, it would no doubt be a pretty cool event for volcanologists and those that like to watch the Icelandic volcanoes.
Some reports of volcanic activity are trickling in regarding 'lava on the ocean floor', and heightened emissions. I am trying to pinpoint a reliable source, so far this has only been mentioned on Jon Frimann's Iceland Geology Blog in his comments section. If true this would definitely explain the large amount of concentrated earthquake activity, as this is a rift zone, prone to seafloor spreading events. I am tracking down his sources to see if they pan out, but so far this is word-of-mouth only at this point.