What exactly were the Japanese trying to accomplish in WWII?

They were trying to obliterate nearly our entire Pacific fleet in one big surprise attack. Had that happened, they could have invaded the US west coast with little to slow them down. Japan was trying to increase it’s territory in Asia, and needed natural resources to do so. It became clear to them that eventually a conflict with the US was inevitable, so they decided to capitalize on the massive strategic advantage of firing the first shot. Unfortunately for them, they didn’t take out the whole Pacific fleet, and things went pretty badly for them as a result.

The Japanese never wanted to fully engage the United States (or Britain) in a full-on head-to-head contest in the Pacific.

Their aim in the Pearl Harbor attack (and the attack on the Philippines and Malay Peninsula, which were coincident with Pearl Harbor) were meant to discourage the US and the UK from engaging them… in the way that they provoked us into doing. (If they had managed to take out the US aircraft carriers, they may very well have succeeded in delaying the strong US response for two or three years.)

Their successful attacks on Singapore and the British Royal Navy did manage to neutralize direct British participation, although Australia and New Zealand participated directly, and India lent a lot of assistance to the overland supply to China (even prior to Pearl Harbor) to fight the Japanese there.

What was happening in the Pacific prior to the attack on Pearl Harbor was a huge Japanese offensive in China, for which they needed massive quantities of oil, rubber and steel, all of which have to be imported into Japan for processing. FDR embargoed US exports of those products to Japan, so they planned to invade Indonesia and Malaysia (primarily) for their needs. They knew that the US would not permit that, so they wanted us to be in no position to respond to their expanded aggression.

Expansion of their empire, as has been said.

The Greater East Asia Co-Prosperity Sphere.
Put more simply, to replace Western imperialism with Japanese imperialism.
They invaded Manchuria and made it a protectorate ten years before they bombed Pearl Harbor.

Thanks to some territory shifting under the Treaty of Versailles, Japan was given dominion over vast lands in Asia. Japan had an empire, which it wanted to expand. There was one problem, however—the United States’s control of the Philippines. The attack on Pearl Harbor was meant to disable the U.S. presence in the Pacific and cause the Philippines to fall to Japan.

They were looking for additional natural resources. They just completely read American reactions wrong. If you don’t understand a culture don’t go after them.

In addition to knocking out the U.S. fleet as a motive, the Japanese considered Hawaii to be within their sphere. Hawaii is closer to Japan than to the U.S. mainland and has for a long time had a large population of Japanese descent.

The Japanese believed, based in many notions but mostly Shinto, that they were destined and entitled to Empire in the East. They also knew that they could not expand their empire or economy without oil. They could not take the territory or resources that they needed as long as the US threatened their rear. They attacked Pearl Harbor assuming two things. That the attack would delay US involvement in their plans until they could establish a defensive position, and that the US would negotiate terms that would allow them to keep some of their gains. They foolishly did not anticipate that the US would demand UNCONDITIONAL surrender. A lesson learned for all aggressors from that point into the present and future.

Access to oil.