The voltage controlled current source charges the capacitor at a rate that is directly proportional to the charging current and hence directly to the input voltage. When the capacitor charges to the upper threshold, in this case 8 V ( 2/3 of 12 V ) at which point the discharge transistor in the 555 discharges the capacitor and the cycle repeats. The brief -ve going pulse at the output of the 555 is connected to a counter in order to provide a square wave ( at half the frequency of the oscillator ) the ramp waveform is buffered by the opamp to prevent the load interfering with the charging of the capacitor.
