What /u/Eponia said.
I would also like to add my own take on the holidays (because I think it's important that there's a "why?" when it comes to holidays within Druidry...and any other religion, too).
In some modern Druid groups you'll hear of the Wheel of the Year. This is also shared by Wicca and lots of other pagan faiths (but by no means do all of them observe the Wheel of the Year).
The Wheel of the Year consists of eight "holidays/sabbats/high days/whatever you call them." These would be the two solstices, two equinoxes, and four other "cross quarter" times intersecting the aforementioned other four days. (So in total you'd have Winter Solstice (Dec 21stish), Imbolc (Feb 1ish), Spring Equinox (March 21stish), Beltane (May 1stish), Summer Solstice (June 21stish), Lughnasadh (Aug 1stish), Autumn Equinox (Sept 21stish), and Samhain (Oct 31stish). Then the Wheel begins again). Here's an example of the visual Wheel of the Year.
The names vary from tradition and person, but in short these are the 8. And I say "ish" on them because the dates vary, especially the Solstices and Equinoxes. The other 4 are just a bit personal preference, really (Some say Imbolc is Feb 1st, and some will say it's Feb 2nd. Then some will say it's the date exactly between Winter Solstice and Spring Equinox). But other Druid traditions don't follow such a Wheel, so it really varies where you're asking. And the above Wheel of the Year is reversed for those in the Southern Hemisphere.
To me it makes sense that modern Druids would observe at least the 4 main ones (Solstices and Equnioxes) seeing that one of the main "functions" of Druidry (to me) is to connect the practitioner to and bring awareness of the Natural world around us. What better way than to get to know its cycles?
