Not to dissuade anyone else from answering, but this thread kind of summed it up.

And a follow up question.

What was the reaction of Russia after gold and oil was found? Had too much time passed for them to really care or was there a sense that they messed up by selling Alaska?

Hey there! This question comes up every other month or so, and I've answered it enough that even Reddit's search engine should find my posts.

There are multiple reasons, but the largest were American manifest destiny, Russia's inability to defend the boundaries of Alaska militarily and economically, and the economic effects of the Crimean War.

After the American Civil War, Secretary of State William Seward attempted to expand American borders politically through purchases. His most successful grab was that of Alaska, but he also attempted to deal with Denmark to purchase Greenland and the Danish Virgin Islands. The latter purchases failed due to the antipathy Congress had for the Johnson administration. The United States ─ at least Sec. Seward ─ was interested in purchasing it.

Russia was interested in selling it because just a decade before, the Crimean War had proved the vulnerability of Russia's extended Pacific possessions. Konstantin, brother of Tsar Alexander II, was head of the Russian Imperial Navy and firmly believed Alaska was indefensible in the event of conflict. It had avoided capture during the Crimean War only because a backdoor deal between the Russian-American Company and the British government (with the help of the Hudson's Bay Company) secured Alaska's neutrality.

While Alaska was a money-earner for the RAC, its distance from European Russia meant Russia had a loose hold on the area. The RAC had to pay for every soldier and priest in the territory, and thus it supported policies that kept Imperial government small. This left Alaska vulnerable to border-jumpers like the thousands of gold prospectors that flocked across the border during the Stikine Gold Rush of the early 1860s.

Konstantin and others in Russia felt the United States was destined to control North America, and if Russia attempted to hold onto Alaska, its possession would either be swept away by the American tide or be a spark for conflict between the two nations.

Konstantin felt that the sale of Alaska would help Russia pay off some of its Crimean War debts while avoiding those problems. Russia sought $5 million in gold, but it negotiated well and was able to get almost half again that amount from the United States.

As /u/TheAshigaru points out, the 1858 Treaty of Aigun was an important contributor as well. With Alaska expensive to operate and vulnerable politically and militarily, the newly acquired Amur River area seemed to offer as much as Alaska did in the way of resources, and it was more secure to boot.

Russia's acquisition of the Amur region through the Treaty of Alguin in 1858 and subsequent events resulting from the Second Chinese Opium War also had an effect on the sale of Alaska.

Over the course of 10 years, Russia gained everything up to its current borders that follow the Amur, Ussuri, and Songacha rivers, along with access to a large chunk of Manchuria which gave Russia access to their former port at Port Arthur (modern Dalian).

In terms of the Alaska deal, this had a major impact because although Russia lost close to 600,000 square miles in that transaction, Russia had also gained approximately 230,000 square miles and additionally had a sort of joint agreement administrating Northeastern Manchuria. This carried a lot of benefit for Russia but not much benefit for China.

So Russia lost territory in Alaska that was difficult to administrate, difficult to protect, unprofitable (although rich in natural resources), disconnected from the rest of the empire, and frozen for most of the year. Meanwhile, they had already gained territory that was connected to the empire, was rich in natural resources, had better port locations (Vladivostok and especially Port Arthur), and had fairly promising agricultural benefits.

There were almost certainly more direct triggers for selling Alaska, but Russia's acquisition of its Southeastern territory also played a major role in the background.