Alternator output is highly non-linear with speed. These curves are for car type machines but the curves will be a similar shape for a bike one.
Typically you'll get little appreciable output power at low rpm. Power is the product of volts and amps. You can draw off power for lights etc but if it exceeds what the alternator can produce at that speed then the voltage will start to drop to the point where you are relying on the battery to supply the balance of the current draw, typically down at basic battery volts of around 12V.
When you rev the engine the alternator output picks up quickly to the point where it can deliver enough current for the load (lights etc) and also start to recharge the battery, at which the regulator will control the voltage in the right region for charging, somewhere around 14V.
lamp resistance increases with temperature so they are not linear either (power vs voltage) but basically as the voltage picks up the current increases and they get brighter.
You don't notice this effect so much on cars because a) the battery has a lot more capability to provide current to supplement alternator output, b) the alternator output is generally just about sufficient at idle to cope with basic demand (pulley ratio etc), c) usually the idle speed is increased slightly by the engine management when electrical demand is applied to avoid flat batteries in traffic. Bikes are a lot more basic.