Since WW2, the US had been occupying Japan and Europe, dumping money and tech into these regions in the erstwhile. The Korean, Vietnam and Cold Wars were good to Japan especially but they were becoming deeply dependent to the US geo-politically and economically. Then the US started to lose their hold after the Oil Shock caused heavy inflation (a stagflation as it was not driven by increase in demand but one of cost) and Reagan stepped up to curb it, with the Fed raising interest rates to 17% in conjunction.

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Loans that were available to businesses and ones they could afford to pay dried up. Foreign money flooded into the US bond market for the prospect of high interest payments while the stock market, which moves in inverse of the bond market, dipped- cutting off yet another means for the industrial sectors to secure funding. On top of these difficulties in production, US goods were no longer competitive due to the currency rates making the products too expensive for foreign markets.

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The US finance sector, in the meanwhile, was having its hay-day with all the Japanese and German proceeds from their exports landing into the US bond market to absorb some of the cost in debt that they were incurring as they were borrowing heavily to manufacture the export items flowing into the US. Ever avaricious, investment banks moved into "fallen angels" and LBOs, which took target companies- not even acquired yet- as assets for collateral. M&As that were designed to flip companies within a span of couple of years by drastically cutting costs ignited the trend of outsourcing and fostered a culture of blowing into bubbles with national debt. In the meanwhile, the conservative Japanese and German bankers just could not keep up and they were facing negative GDP growth.

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So the US wanted to get US exports back on the board by devaluing its currency. Japan and Germany wanted to prevent a punitive tariff as well as gaining a hold of their rampant debt, which would now be easier to pay. Japan also had ambitions for the yen to become the new dollar as the Little Dragons and the Tiger Club were just beginning to sprout. And since they were selling high-end manufactured goods like cars while importing commodities like food from the Americans, they were confident that they could take the hit on their own exports by setting up operations in the US and so on. They obviously weren't aware of the trillions of long positions on their currencies laying in wait.

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While the Japanese were quite eager to sign the Plaza Accord at the time, the move has been widely considered, especially in Japan, as the cause of the Lost Decade. Since Japanese goods had basically doubled in price over 2 years, their export-oriented economy suffered. Interest rates were cut to help but the free money flowed into stocks and real estate instead of the bottle-necked businesses. The inflation got so bad that Japanese real-estate metastasized into $18 trillion (4x all of US) and the imperial grounds in Tokyo was considered more valuable than all of California. When interest rates were raised to stem the inflation, the bubble burst as it does in any financial crisis. However, cost of living had gotten so out of hand that the birth rate had already been dented beyond help and the shrinking workforce, to this day, fails to drag the Japanese economy out of the hole.

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TL;DR- The Oil Shock caused stagflation and crazy high interest rates were used to get out of it. The US wanted to devalue its currency to even out their trade balance, making their exports cheaper in other countries. But Germany and Japan, who had been riding a high from the US being out of the fight, had incurred enough American debt to hurt their GDP growth and were, too, eager to get to the negotiating table. Japan, especially, was looking forward to becoming the new dollar.