The depreciation of the U.S. dollar (USD) with respect to the Japanese Yen (JPY) increases the number of USD that a person can buy with a given number of JPY. Conversely, a person with USD can buy a smaller number of JPY.
When exporters from Japan sell their products in the US, the payment they receive in the US is in terms of USD. The USD is then converted to JPY at the prevailing exchange rate between the two countries and transferred as JPY to Japan. If the USD depreciates with respect to the JPY, a Japanese exporter receives a smaller payment in terms of JPY for the same article sold. The result of this is a drop in exports from Japan to the US. From the point of view of an importer in the US, due to the depreciation of the USD, buying the same article from Japan is now costlier in terms of the number of USD required and this decreases the import of Japanese products in the US
On the other hand, due to the depreciation of the USD exports of US products to Japan is increased as an exporter in the US gets more in terms of USD and a Japanese importer is able to buy US products at a lower rate in terms of JPY.