As has been said, its mainly about how efficiently you can evacuate spent air from your lungs and suck in more oxygen rich air.
Lower flow = lower exchange of air = lower blood oxygen saturation all of which will have an effect on your performance.
This is kind of true, but only in extremes of asthma attacks.
If you have a slightly reduced peak flow, you'll have normal SaO2 (sats) levels.
What is peak flow....
It's a measurement of the maximum 'speed' you can exhale air at.
It doesn't measure how much air you blow out (this is lung capacity, which can be measured on a different machine), but...obviously if you have tiny lungs, you'll blow out less air, which will 'move' the peak flow 'spring' less (which is why peak flow charts are based on height/sex.)
Peak flow can be reduced by airway obstruction (purse your lips and try and blow out forcefully - the air comes out at a piffy rate doesn't it - this is just a 'narrowing' at the lips, but in asthma ths narrowing occurs 'inside the lungs' but has the same effect. Try breathing hard for 1 minute through pursed lips - not nice is it...!)
However, peak flow can also be reduced by 'illness causing reduced lung capacity', and poor peak flow technique.
Spirometry is the 'gold standard' test as it compares FEV1 (forced expiratory volume in 1 second - how much air you can blow out in one second) against your FVC (forced vital capacity - how much air in total you can blow out to completely empty your lungs). It's the comparisons that's useful, but of course this is a fancy and time consuming test, and in the majority of cases, peak flow is great as it compares yourself against yourself...!!
Essentially, a low peak flow (i.e. poorly controlled asthma) will make sport and activity harder)