Essentially this is a workaround for a limitation in Ableton Live, in that Live reports rounded tempo values to hosted plug-ins when externally synced by MIDI clock. For example, if Live receives clocks at a tempo of 114.6bpm, it will tell its hosted plug-ins that the tempo is 115bpm. Why it does this remains something of a mystery.
This is a problem if you are using multiple instances of Augustus Loop in a Live song, with one AL set to generate MIDI clock, Live synced to that clock, and the other ALs set to 'Host Tempo' mode. When you use Tap Record to record your loop in the master AL, the other ALs will be given a slightly wrong tempo by Live and the loops will be out of sync.
Turning on 'rounded tempo' in AL solves this problem by only ever generating MIDI clock at rounded values. The downside is that the loop length will not be quite what you wanted, but it may be good enough, depending largely on your musical style and whether you record the first loop 'silent' simply to set the tempo.
With this mode turned on, when you use Tap Record the loop end will be slightly later than when you tap to close the loop. E.g. if you record a loop that would have a tempo of 122.3bpm, AL actually keeps recording until the loop length matches a tempo of 122bpm.