The circuitry to recharge the batteries in a portable product such a mobile phone plays an important part in determining the battery longevity and the practicalities of using the product on a daily basis.
The charging protocol (how much voltage or current for how long, and what to do when charging is complete) depends on the size and type of the battery being charged.
The modern battery chargers adapt the charging parameters dynamically based on the level of charging the battery has reached. An empty battery can be charged faster without any safety risk. This is why most benchmarks for charging speed (ours included) quote the battery charging level reached after a 30-minute charging session on an empty battery.
With basic chargers outputting 5V/1A equalling to 5W of power, anything faster than that is considered quick or fast charging.