From a recovery standpoint, the log backup chain links the Last LSN of one backup to the First LSN of the next. If the first & last LSN in a log backup are the same, then it means that this log backup is effectively empty of transactions.
Take this simplified example:
Log Backup Time | First LSN | Last LSN
---------------------------------------
1:00 AM | 0001 | 0010
1:30 AM | 0010 | 0020
2:00 AM | 0020 | 0020
2:30 AM | 0020 | 0030
In this example, you can restore all four log backups in the order they were taken, however, the 2:00 AM backup is not strictly needed. Because the LSNs link the 1:30 AM backup directly to the 2:30 am backup, it would be possible to achieve proper recovery without restoring the (empty) 2:00 AM backup.