A simple application of the resistance formula will show you why.
It is easily found that the hot resistances of the 60 watt and 100 watt bulbs are 240 ohms and 144 ohms respectively. That is a series total of 384 ohms and a series current of 120/384 or 0.3135 amps. That makes the power dissipation of the 60 watt and 100 watt bulbs in series 23.44 watts and 14.06 respectively. Since the 60 watt bulb dissipates almost twice the power of the 100 watt bulb, it is a good assumption that it will appear brighter.
In reality there is actually a greater difference between the two bulb's power dissipation than Ratch's linear calculation shows. That is because the resistance of a tungsten filament typically varies more than 10:1 from room temperature to its operating temperature. Thus, when connected in series, the cooler 100W bulb filament will actually be at a lower percentage of its normal hot resistance than the 60W filament