A 4500 PSI tank is referring the pressure that a compressed paintball air tank can hold. When someone uses the term PSI, they are referring to Pounds per Square Inch. The higher the pressure, the more shots you will be able to get off one fill.
Most carbon fiber bottles are considered to be 4500 tanks which is the maximum an air tank can hold. Less expensive and heavier aluminum tanks usually have a maximum pressure rating of about 3000psi.