Historically, Samhain was an Irish Celtic harvest festival that marked the beginning of the winter season. It is not likely to have been held on a specific calendar day, but rather whenever the harvest was finished for the year.
Connections between Samhain and HalloweenThere are a variety of Halloween traditions often credited to Samhain, such as costume wearing and the creation of hallowed out vegetables (predecessors to the jack-o-lantern). Readers are cautioned to be very wary of such claims. The Irish were non-literate before the coming of the Romans and even then left us no documents about their society. Most of what we know of them therefore comes from outside sources, often people who had never actually met the Irish or, more often, were writing hundreds of years after their pagan society had vanished.
In addition, the common claim is that ancient Celtic practices became folklore practices in the Christian period which is how they were transformed into modern Halloween celebrations. Again, the evidence of often sketchy, with most of it dating on a couple centuries back. Many of these claims of Halloween celebrations being ancient are therefore conjecture at best.
Samhain in MythologyFrom the mythological stories (again, written many centuries after Christianization), Samhain appears to be a time of transitions when chaos reigns. The are references to the closeness of the Otherworld to the world of the living during this time, and it is commonly associated with divinations and remembrances of the dead. The mythology rarely if ever touches upon specific rituals performed by common people.
Modern Samhain CelebrationsToday, a variety of neo-pagans celebrate Samhain. Many celebrate it the night of October 31, but some calculate the date via other methods such as astrologically or even by when local harvests are completed. Some even refer to the holiday as "Halloween" rather than as "Samhain," which merely further confuses the issue.
Modern celebrations manifest in a wide variety of ways. First, they may reflect mythology and beliefs specific to the celebrating neo-pagans. Wiccans and Druids, who belong to two separate neo-pagan religions, might hold significantly different celebrations, for example. Second, they frequently reference Northern European folklore or Celtic practices as they understand them to have been (which may or may not align with what was actually historically).
Modern Samhain celebrations are certainly not part of an unbroken pagan tradition. In fact, they post-date the secular emergence of Halloween.