These PCs are known as bots. A botnet is a network of computers that wait to be commanded remotely.
Whoever controls these PCs can install and run software without the PC owner ever knowing. He can also spy on his victims and get login details or even credit card details.
Joshua Schichtel is a 30 year old man from Arizona. He hacked and virused thousands of PCs. The botnet had 72000 PCs. Instead of using the botnet for himself he had a different idea. He basically rented it to wealthy individuals or companies. The PCs in the botnet ended up having even more malware installed and Schichtel made a fortune of unsuspecting victims.
The hacker was brought to justice and got 30 months in prison sentence because he violated other people rights under the Computer Fraud and Abuse Act.