There's actually a very legendary reason for the initial settlement in Iceland being in Reykjavík (current capital). When the first settler, Ingólfr, was on his voyage to Iceland at the first sight of land he commanded his slaves to toss his high seat pillars into the ocean (these type of intricately carved wooden pillars were at each end of the high seat in a house in Nordic societies, indicating that he was indeed a wealthy man back in Norway before he journeyed to Iceland) and when he arrived on land he commanded his slaves to circle the coast until they found the pillars. Where the pillars would end up, there he would permanently settle. It took a couple of years for the slaves to find them but they eventually did in Reykjavík. Ingólfr moved there, gave it its name for the smoke (Reykjavík translates to Smoky Bay, even though it was actually steam) he saw rising from the ground, freed his slaves and built his home.

Fast forward a 1000 years and now Reykjavík and its surrounding areas contain 2/3 of Iceland's population.

Another more practical reason is that the East is quite barren with volcanic deserts and rocky fjords, not great places for settlements. Reykjavík is situated on a flat peninsula in a cozy bay.

That's probably a later development, for hundreds of years the population was spread pretty much evenly across the country (where there was habitable area, anyway. Habitable area wasn't stable through hundreds of years though due to volcanoes, earthquakes and a drop in temperature from the age of the settlers (850-1100), where it was higher than it is now, to the 18th and 19th century, in which it was colder than it is now).

When Icelanders stopped being only farmers and started forming villages along the coast Reykjavík wasn't the only one, and not even the most populous one I think I remember correctly. In any case it was far from being so much larger than anything else as it is today. But starting in the 19th century and continuing on to the 20th century people started moving to Reykjavík in large droves from all over the country. Also, at the end of the 19th century, a large percentage of the Icelandic population moved to the USA and Canada.

So the basic answer is that western Iceland being much more heavily populated than the east is a recent development, caused by people stopping being farmers/seamen only and starting forming towns and villages...which only happened a 100-150 years ago, very late compared to other nations around us.

I apoligize for not providing any sources, I'm just an Icelander writing from memory. I could probably find something better later when I have more time.

Edit: Why Reykjavík? Not because of Ingólfur Arnarson, sorry. It was probably because the Danish had their "headquarters" at Bessastaðir near Reykjavík. Why the Danish chose to govern from that area I don't remember learning.

hi! while you might get answers here, this isn't so much a history question as one of geography & habitability; it might be worth x-posting to /r/Iceland to ask the locals