... I don't even know what 's a network adapter .
How do you connect to the Internet at the moment? You are either connected through a Wireless Network or through a network cable connected from e.g. a router to your PC/Laptop. In both cases a network adapter (wired or wireless) is requires in your system.
Regarding the error message. ESXi is build for server hardware and only contains drivers for supported network adapters. You either need to add such a network adapter to your system or - in case you only want to evaluate ESXi - you could install ESXi as a virtual machine in VMware Workstation.
André