I've heard it said that 'head voice' is 'lighter' than 'chest voice'. As in, when you go up into your head voice, you 'shed' some of the 'weight' that you have in the chest voice, which allows you to go up to higher notes more comfortably, without having to 'lift' the weight of the chest voice.
I'm speculating a bit here, but my guess is she is talking about chest voice vs head voice. Most men (to my knowledge, and I am assuming you are a man) speak in their chest voice, rather than their head voice. So, it makes sense that she's saying your singing voice above the speaking range should be 'lighter'.
Thinking objectively, head voice is 'lighter' than chest voice, because you are resonating a smaller volume of air (in your head), as opposed to a larger volume (in your chest). It's a bit like playing a bassoon vs playing an oboe. Try and get up to a fairly high note with a bassoon, and you're going to have quite a hard time (and probably wear yourself out). But, try it with an oboe and it will be much easier to get to that higher note. I think the analogy also extends to the sound quality - a bassoon sounds deeper and 'heavier', while an oboe just 'sounds' lighter, because of the difference in the resonant volume.
I'm not sure why she is recommending that you start warming up above your speaking range though. I've been warming up my chest voice first, then going up into head voice, which seems to be working for me. I'm not a professional vocal coach though.