According to Apple's documentation, "This SMC firmware update adds compatibility for the latest service replacement batteries.... After this update has successfully completed, your SMC Version will be: 1.23f20 [for original MacBook Air models, or] 1.34f8 [for more recent models]."

In general, update the System Management Controller on Intel-based Macs. The SMC controls power and thermal management features, including the battery and fans. In this case, new replacement batteries from Apple are apparently different enough that they require the use of this updated version of the SMC firmware.