Ron Guth: In 1873, Mint employees used a date logotype where the loops of the 3 were so close to each other that the date could have been confused for an 1878. Later in the year, a new logotype was created with loops of the 3 moved farther apart. The Nickels weren't the only coins affected by this change -- quite a few other denominations were, as well.
In terms of relative rarity, the Closed 3 is clearly the scarcer of the two varieties. According to the PCGS Population Report (as of June 2011), PCGS had certified 66 Closed 3 and 222 Open 3 1873 Nickels in all grades. Among the Closed 3 variant population, MS-64 is the most frequently-seen grade. The finest examples certified by PCGS were three in MS-66.