In general, it means a fresh sausage meant to be cooked, as opposed to salame, which are generally cured and ready to eat. Roman writers gave the credit for their invention to the ancient Lucanii, who lived in what is now the Basilicata, and lucanica or luganega is still a common name for them.
As you would expect, Italy has hundreds of different recipes all over the country. There are sausages of pork, beef, turkey, goose, buffalo or any mix of the above, liver sausages, offal sausages, sausages with greens or pine nuts inside, boar and deer sausages, sausages flavoured with honey or fennel (very popular) or coriander or peperoncini.
Sometimes it's hard to know where a salame starts and a salsiccia ends. Famous salsiccia di Calabria (Casanova really liked it) is really a salame.
Image by Julien Menichini