During a recession, there is an inefficient use of resources both in terms of labor which can be seen from the fact that unemployment rises and in terms of other resources with factories lying shut down and machinery not being used.
To stimulate aggregate demand, it is essential to bring in more money into the country. The money in the hands of people would allow them to start buying more goods and services and hence boost consumption of the produce of domestic industry. This increases the money available with people more and a cycle out of recession is created.
The exchange rate determines whether a country's goods and services are bought by people in other countries. If your country can deliver the same product at a price less than what can be delivered by another country, your exports are going to rise. A way to do this is to decrease the value of your currency and allow citizens of country X to get 10 dollars with one unit of their currency instead of 1 dollar. Now, they can easily buy a product that you export which is worth $10. This boosts demand for your exports. Also, as people find importing products exorbitantly expensive, it would increase their consumption of goods manufactured by industries within the country.
In this way the exchange rate policy can stimulate aggregate demand during a recession.