This type of Penetration Testing is typically done to simulate what an attacker that has made their way into your network can gain access to.You will typically be on site and connected to the network or remotely connected and be given rights to break into as many machines as possible and find valuable information.
This type of Penetration Testing is typically done from outside of a network and tests the ability for hackers to break in from the outside. You will typically conduct these kinds of tests with public IP addresses for the network and try to break in.
This type of Penetration Testing focuses on attempting to exploit vulnerabilities in a web application or a website to see where it may be vulnerable. It is important because if a company is offering an application online that collects private information to people, they need to know that their application is safe.