Explain the calendar in Skyrim

The Tamrielic calender is simply a Gregorian calender with different names, and without leap years.

From the UESP:

Midyear, Hearthfire, and Frostfall are not consistent even within the games, alternating between references as a single compound word (i.e., Frostfall), and a pair of words (i.e., Frost Fall).

Furthermore, Hearthfire is referred to as Heartfire in Skyrim, despite some lore books continuing to list it as Hearthfire. (The last time it was referred to as Heartfire was in TES:Arena, so it's possible this is a regional dialect)

According to the UESPWiki.

Days

• Sundas = Sunday
• Morndas = Monday
• Tirdas = Tuesday
• Middas = Wednesday
• Turdas = Thursday
• Fredas = Friday
• Loredas = Saturday

Months

• Morning Star = January
• Sun's Dawn = February
• First Seed = March
• Rain's Hand = April
• Second Seed = May
• Mid Year = June
• Sun's Height = July
• Last Seed = August
• Hearthfire = September
• Frostfall = October
• Sun's Dusk = November
• Evening Star = December