The short answer: it sets a tempo for an internal oscillator.
The long answer:
You can assign time-based effects to take their rate of change from this tempo value instead of setting the to a fixed value. This would, for example, let you tap a footswitch (or that button on the front of the unit) to see the rate of a chorus block, the speed of a tremolo block or the time between repeats of a delay block.
In the delay block, you can tell you're locked to the tempo and not a fixed time value, by check the Time parameter:
If it has the time in brackets like that, it's taking the time from the tempo assigned to the unit and it means you can modify it in real time while you're playing by tapping that button or a footswitch your external controller. The drop down menu to the right of the Time parameter lets you set up a divisor or multiplier for the tempo. You could, for example, tap on the quarter notes but have the Time value set as if you were tapping on the eight notes or sixteenth notes. In the picture above you can you see that it's set to dotted eights -- so taps on the quarter notes set the tempo, but the time value is set so repeats happen on dotted eights relative to that tempo (this is the "U2 time" for repeats...it's very popular for playing rhythmic delay type stuff).
You can use the tempo to set the frequency of the LFO 1 and 2 oscillators in the controllers section of the Axe-Fx -- and then assign these controllers to any controllable parameter -- and give yourself tap-tempo control over just about anything. Like maybe you want to get whacky and have the drive parameter of a drive block change according to some specific frequency as you play as an example.
One of the more interesting things you can do with this magic black box is you can have multiple effects set to take their tempos from this internal value and "sync" them up in really nice ways. For example, you can have a sync'ed delay and tremolo block which can you do you neat things like this:
That intro, poorly played by me sorry, isn't possible without time-aligning the tempo and delay.
