I don't understand what's written in the datasheet (see here on page 3):
Input Voltage Range: min 0.9 Max: Vf-0.2 (Note 1) Note: 1. VF - LED forward voltage.
What does that mean?
First you need to understand what this device does. From both the description and the typical application circuit, we can see that this is a boost converter with output current regulation. That makes sense since it's purpose is to drive a LED from one or two batteries.
One important parameter you need to know is what input voltage range it works over to drive a particular LED. The part you quote tells you exactly that, and quite unambiguously. The answer is that the device needs at least 900 mV in to operate, and the input voltage can be up to 200 mV below what the LED runs at.
For example, if you are driving a LED that drops 3.4 V at the regulated current point, then the input voltage needs to be 900 mV to 3.2 V.
I didn't read all of it, but the datasheet seems to be well written and clear. I really don't see where the confusion is.