1. The network portion of an IP address. For a class A network, the network address is the first byte of the IP address. For a class B network, the network address is the first two bytes of the IP address. For a class C network, the network address is the first three bytes of the IP address. In each case, the remainder is the host address. In the Internet, assigned network addresses are globally unique.
2. (Or "net address") An electronic mail address on the network. In the 1980s this might have been a bang path but now (1997) it is nearly always a domain address. Such an address is essential if one wants to be to be taken seriously by hackers; in particular, persons or organisations that claim to understand, work with, sell to, or recruit from among hackers but *don't* display net addresses are quietly presumed to be clueless poseurs and mentally flushed.
Hackers often put their net addresses on their business cards and wear them prominently in contexts where they expect to meet other hackers face-to-face (e.g. science-fiction fandom). This is mostly functional, but is also a signal that one identifies with hackerdom (like lodge pins among Masons or tie-dyed T-shirts among Grateful Dead fans). Net addresses are often used in e-mail text as a more concise substitute for personal names; indeed, hackers may come to know each other quite well by network names without ever learning each others' real monikers.