The dollar depreciates in value when a dollar is worth less relative to another currency. A dollar appreciates in value when it increases in value relative to another currency. Currencies globally depreciate and appreciate relative to one another based on the economic conditions in the countries where the currencies are used and investor sentiment.
The dollar depreciating relative to another currency means that exports from the US to the country that uses the other currency will expand, and imports from that country to the US will contract. If you primarily use the other currency, goods priced in dollars have become cheaper, which leads to expanded exports from the US to the other country. If you primarily use dollars, goods priced in the other currency have become more expensive, which leads to reduced imports from the other country to the US. The dollar can appreciate versus some currencies while depreciating versus others, which means that this type of analysis can be very detailed to determine the total change in aggregate demand.
If human economic behavior is rational, households that expect lower prices in the future will tend to spend less and save more. Then when prices are reduced, the households will spend more, as their money will go further. The reality is much more complicated than this simple view, because human economic behavior can often be emotional even on the aggregate. For example, buying a car every year even though the car will drop significantly in value is not rational, but many people do it anyway. However, in general, a drop in prices will lead to more consumer spending.