They had several goals, and trade was one of them. China produced a ton of exotic goods that sold well in Europe, and it was the peak era of 19th century colonialism. Japan wasn't nearly as rich and only had a couple of exports, but the US was more interested in them as an additional market in which to sell US goods. The west coast was getting a lot of new migrants, and the transcontinental railroad was 10 years away. Without access to the canals and rivers of the East coast, they needed someone to sell to.

The other major stated reasons for the expedition were more practical. Steamships were just starting to be a thing, and everyone was trying to get places to refuel. The US was interested in trading with China, but other nations like the British, the French, and the Dutch had monopolies on the coaling stations in the area. So the US would be really happy if they could just have somewhere in Japan they could stop and get some coal.

The other practical concern was castaways. The US at this point was in the middle of their whaling boom, and one of their big fishing patches was near Hokkaido and northern Japan. When someone fell overboard, they wound up on a Japanese beach. While anyone entering or leaving Japan was illegal, usually the Shogunate or local Daimyo would take these castaways into custody and bring them to Dejima in Nagasaki where they could leave on the next Dutch ship. However, there had been one or two incidents where the castaways tried to escape (presumably panicked about being captured in a strange land with few English interpreters). After being recaptured, those sailors were then kept in bamboo cages, and several died of exposure. When word of this got back, it led to stories of maltreatment, abuse, executions, etc. So one peg of the treaty was to establish rules for the return of American maroons.

In general though, there was an undercurrent of not really respecting the sovereignty of Japan when it came to the sakoku edict of keeping the country closed. By the late 19th century imperialism was in full swing, and global trade had been roaring for hundreds of years. The Shogunate was looked down on as very backwards thinking for their desire to keep the country closed. Part of this was because Japan was such an unknown the Americans had almost no idea of the internal political situation (they didn't even figure out exactly what the deal was with the Emperor until later), and just couldn't understand why the Japanese wouldn't want trade.

Bear in mind, there had been several attempts to open the country less forcefully with the help of castaways from a Japanese fishing ship, but they had all been repelled upon arrival, sometimes violently. The US felt like they weren't even being given the time of day and they were sick of this shit, so they sent a military fleet instead of a smaller expedition of merchants and diplomats like previous attempts.