There are lots of information about responsivity, start condition, integration, serial interface, and normalized responsivity are described in this datasheet. Inside this datasheet you can find info around ambient light, light, intensity, and light source.
This datasheet contains explanation such as threshold, range, gain, and light emitting diode. Here are grabbed from the datasheet:
The TSL2560 and TSL2561 are light-to-digital converters that transform light intensity to a digital signal output capable of direct I2C (TSL2561) or SMBus (TSL2560) interface. Each device combines one broadband photodiode (visible plus infrared) and one infrared-responding photodiode on a single CMOS integrated circuit capable of providing a near-photopic response over an effective 20-bit dynamic range (16-bit resolution). Two integrating ADCs convert the photodiode currents to a digital output that represents the irradiance measured on each channel. This digital output can be input to a microprocessor where illuminance (ambient light level) in lux is derived using an empirical formula to approximate the human eye response. The TSL2560 device permits an SMB-Alert style interrupt, and the TSL2561 device supports a traditional level style interrupt that remains asserted until the firmware clears it.
Even more, the datasheet gives the reader info about adc, light intensity, read write protocol, and protocol.