What does voltage connector's voltage rating mean? AC-rms or AC-peak voltage?
The voltage rating is 300V rms if the applied voltage is AC. The voltage rating is 300V if the applied voltage is DC. These are ratings, and more importantly use ratings. If you look to the bottom of the data sheet, you'll see UL recognition E60389, and two other certifications.

These are not breakdown voltages for the connector. If you look a few lines further down you will see 'withstand voltage 1500VAC (that is, 2120 peak) for 1 minute'. 

In use, this connector may be connected to power for 10s of years continuously. The mechanisms for insulator failure over those timescales are different for AC and DC, and involve differences in how defects propagate through the plastic, and how surface contamination is attracted. The consequences for breakdown are also different, with an AC arc being easier to extinguish due to its zero crossings than a DC arc. These explain the difference between the AC peak and the DC rating.

So what the ratings mean are 'even though you can put 2120V on here for a minute, if you keep the long term voltage between +424V and -424V if the voltage is changing polarity, and between 0 and 300V if it stays the same polarity, then you can use this connector in equipment that you certify complies with UL requirements, based on identifying the components alone, and without further testing of this connector.' The apparently large standoff between the withstand and the use voltage is necessary for the difference between 1 minute for a new connector on the bench, and one lifetime for a connector in equipment in possibly hot, damp, dirty, contaminated conditions. 

The importance of UL ratings are that it stands for 'Underwriters Laboratories', that is, insurance. If your factory burns down, and you sue me, the supplier of the equipment that started the fire, and I'm found to be exceeding the rating on a connector, then my insurance is not going to pay out. Ideally what happens is I should not be able to get a license to sell my equipment in the first place, if I am using components beyond their ratings.