K-line is an IRC term. It stands for a line in the configuration file of the IRC server (ircd.conf), that prevents a client with a specific hostmask from connecting. Such a user is then called 'k-lined'.
Reasons for a client being k-lined may include:
Geography: If a IRC network has servers in different countries and continents, it will try to reduce the distance between server and client. Thus, servers on one continent may k-line all clients from the others and vice versa.
Infected client: A client infected by a virus, worm or trojan that spreads via IRC may be k-lined, so it doesn't reduce the efficiency of the server and to decrease the rate at which the malicious program is spreading.
Misbehaviour: If a user repeatingly disobeys the rules of the IRC network, and doesn't change his behaviour through kicks and bans, then he/she might get k-lined to protect the other users of the server.
Abuse: Users who use the network for spamming (advertising a particular web site, or sometimes displaying false news alerts, often about terrorism) are frequently k-lined. Other forms of network abuse may also result in this effect.
The following terms are also related to k-lines:
A g-line is a network-wide k-line.
An akill or "Autokill" is a network-wide k-line that is done through Operserv
A q-line is a ban on a nickname on a server
A z-line is a blocking of an IP address range on a network