(I meant to post this on August 5th, the summer/fall cross-quarter day, but was late.)
The following includes both others' ideas and my own. Good things are always the work of many hands.
The Pagan Wheel of the Year consists of eight points: the solstices and equinoxes; and the midpoints between them, called cross-quarter days. This makes four pairs of opposite points.
Each of these pairs is characterized by a pair of opposing principles, and in each case we celebrate the day, or the season, with the quality opposite to the one characteristic of the time being observed.
The following assumes the northern hemisphere.
The summer solstice (Midsummer) is the longest day of the year, and the winter solstice (Yule) is the longest night. This is the axis of light and dark. Summer is the time of greatest daylight, and so the midsummer celebrations take place at night. Winter is the time of deepest darkness, and so we celebrate with lights: Christmas lights are a staple winter decoration; Hanukkah, the festival of lights, occurs near the winter solstice; the cold brightness of sun on snow is a staple Yuletide image.
Spring and fall (equinoxes Ostara and Mabon) are characterized by the axis of birth and death, because life blooms in spring and withers in fall. Easter, which takes place in spring, is a celebration of the sacrificial slaughter of the god; spring cleaning is an emptying, causing things which were there to be there no longer: a positive destruction. Fall is celebrated by acts of creation: carving jack-o-lanterns, dressing in costumes, arts festivals.
The winter-spring and summer-fall cross-quarter days (Imbolc and Lunasa) are characterized by cold and heat, as they fall in February and August, the middle of the coldest and hottest parts of the year. Secularly, the cold season is traditionally associated with hot chocolate and sitting around the fireplace; the hot season with iced tea, lemonade, and ice cream.
Finally, the fall-winter and spring-summer cross-quarter days (Samhain and Beltane, in November and May) are characterized by dry and wet, again due to the nature of their seasons.
Construction of appropriate ritual observances for the cross-quarter days is left as an exercise for the reader.