Solar panels collect the light that hits the earth from the sun. They convert the light into power that is either stored in batteries or used straight away, for example a toy car or desktop gadget.
Solar lights use the power from the batteries that the solar panel has collected during the day. They typically use LED bulbs to provide light as these are the most efficient way of converting the power back into light.
At dusk the lights sense the reduction in sunlight and turn the LED bulbs on. Modern lights often have an on / off switch allowing you to override this setting if you don't want the lights to turn on.
Solar products more often then not have batteries to store the power collected during the day for use later when required. Solar Lights are probably the best example of this, other notable product types include solar phone chargers.
These have an internal battery that you can have on standby to get your phone back up and running if you're caught short without a wall charger nearby.
Think about rain falling on two buckets placed side by side. A bigger bucket will collect more water then a smaller bucket from the same length of time in the rain.
With solar power the solar panel and batteries represent the bucket. The panel collects the light, converts it to power and stores it in the batteries. Typically the bigger the solar panel the more light is collected.
Matching higher capacity batteries with a more powerful solar panel has two main benefits.
More power is collected during the day.
Any excess power can be stored in the batteries for use the next day - this means the batteries may not start each day from flat giving you the product a head start on a cloudy day in terms of performance in the evening.
Other factors can have an effect such as the:
efficiency of the panel
type of solar panel
capacity of the batteries
type of batteries used
Check out this guide to getting the best from your solar powered products.