The word net is an abbreviation for network. In the Amateur Radio community, nets are groups (networks) of hams with common interests. These groups meet on the air at designated frequencies and times. Some nets meet daily while others convene weekly. Nets aren't  just an HF phenomenon there are VHF and UHF nets, too. Voice and CW are the most common modes for nets. There are also RTTY nets and packet nets. (Packet nets often use conference modes which allow many packet stations to connect and chat at once.)

Whenever you have a bunch of hams together on one frequency, the greatest challenge is avoiding chaos. That's why most nets appoint a net control station, or (NCS) The net control station acts like a traffic cop, directing the flow of the meeting and keeping confusion to a minimum. When its time for the net to begin, the NCS "calls" the net. If you're listening to a voice net, you might hear something like this.
This is KJ4BOJ, net control station for the North Brevard A.R.C. conducting the friendship/ARES net. This net meets on each Tuesday of the Month at 7PM on this frequency.
If the net sounds interesting, why not join in? Just transmit your call sign. When the NCS hears you, he will say your call sign, and you will be added to the list of net stations. The NCS usually acknowledges you by repeating your call sign. If he does not acknowledges you, repeat saying your call sign again until he acknowledges you. Sometimes its hard to get all the call signs down when everybody is transmitting at the same time. Nets using other modes, such as CW, often use different procedures. Its best to monitor the net for several minutes until you get a feel for how it is managed.
Many HF nets ask for check-ins by call-sign areas. ("Stations of the fourth call area, please come now.") Other nets have an existing roll call of stations who participate on a regular basis. ("Call signs ending in a letter please come now.") or (calling the call signs on the list.) After these stations are check in, the NCS will ask for "any other check-ins" If you new to the net that is your invitation to join!
Once you're checked into the net, stay close to the radio and listen carefully. Soon the NCS will begin reading through the list , calling each station in turn. Don't worry if you have nothing to say when the NCS you, then just say this is your call sign ("Nothing for the net or no traffic."

If you have to leave the net, make sure to let the NCS know. In voice nets, this is as easy as saying "check out" between someone's transmissions. The net control will pause and ask, "Who's the station checking out?" Give you call-sign and say ("Please check me out")
There are more varieties of nets than Baskin-Robbins has flavors of ice cream. National Traffic System (NTS) nets meet to pass messages from one area of the state or country to another. Because of the volume of messages that must be moved, these net tend to be very formal, you'll also find Amateur Radio Emergency Service (ARES) nets. They're devoted to emergency preparedness. When disaster strikes, these nets become important links for lifesaving communications.
DX chasers have there special nets. They meet to arrange contacts with desirable DX stations. There are nets for Satellite enthusiasts, railroad buffs, military veterans, computer users, slow scan TV and fax operators, and just about any other groups or purpose you can imagine.
Nets provide excellent opportunities to make new Amateur Radio friends. Listen to several nets and find a couple that sound interesting. Check in regularly and pretty soon you'll become familiar with all the other participants. Don't be surprised if you find yourself looking forward to each net session. Some hams schedule their lives around their favorite nets. (Convenient Excuse #446: "I can't cut the grass. The net is on!"