The economy is important to households, consumers (these two are essentially the same thing), and firms because it determines the sorts of opportunities those groups have to make money and to buy goods and services.
Households and consumers can be seen as the same thing. These are both made up of individuals who sell their labor to firms and who buy goods and services from those firms. The economy matters very deeply to these people. People in households need money. In order to get money, they have to sell their labor to firms (or to other producers like government agencies). When the economy is poor, it is harder for them to do this and their economic prospects dim. The economy also impacts their ability to consume. When the people are able to work, they have more money to use to consumer. When the economy is strong, there are generally more things for them to consume as more firms are making more things.
For firms, the economy is important as well. When the economy is strong, firms have more opportunities to make money by selling goods and services. Consumers have more money and are more willing to buy so firms can produce things to satisfy those demands. When the economy is strong, there is more money available to borrow and so firms can expand their capacity to produce.
In all these ways, the economy is very important to consumers and households on the one hand and firms on the other.