Thank you dear lord for beinging 60YOC into this world!
You see, what he says is that instead of fearing the conversational (or otherwise) tension, you should start enjoying it. How? Don't feel awkward while you have nothing to say, nor should you feel the need to say something. Wait for HER to say something
Let HER become concerned with the tension. You should sit back relaxed, smiling at her little slips and misses here and there 
The more you try to invest in these awkward situations, the lower goes your status. As you might have observed, even if you do end up coming up with something, it's usually very lame and doesn't carry the conversation forward very well. Instead, let her say something 2 out of 3 times, the third time, you release the tension for a change
Also, if your relationship is a serious one and there is a good level of understanding between the two of us, you'll start to appreciate the moments of silence as well. Just.. snuggle up with her or start caressing her shoulders or arms gently.. build a stronger rapport during such moments. Good Luck.