Basically, it's saying that consumers used to dictate prices but now companies do, and this is debilitating to the economy.
Like... a consumer simply wouldn't buy something if it was too expensive.
So in order to sell goods, companies had to meet the pricing expectations of consumers.
However, because companies are so powerful now, it's them with the power and not the consumers ("selling power" instead of "buying power").
I understand economics better when I have examples, so I shall endeavor to paint a colourful story XD (Okay... maybe black and white... not colourful... economics isn't *that* interesting)
In the good ol' days of the town marketplace, if one baker charged less for their bread than the other and the bread was of equal quality, you'd most likely wander over to the cheaper baker and buy your bread from him. Think now about Coles or Woolworths. If they charge $4 for a loaf of bread instead of $2.10, what are you gonna do? Unless there's an Aldi nearby, you're most likely gonna fork over the $4.
Think of this now as applying to all food, not just bread - what are you going to do? You need to eat, so you're highly likely to continue to buy food anyway, despite higher prices. Because Coles and Woolworths (and other companies in general) are so large-scale, they can dominate and manipulate the market in this way. Obviously, there are limitations to this "market power" - I've already mentioned competition as an example (Aldi).
It goes further than this too. Say that it costs Harry $1 to make a loaf of bread, and Fred $3 to make a loaf of bread. In an efficient market (the market in the good ol' days where you buy from the cheapest baker) where consumers will pay no more than $2.10 for a loaf of bread, it is quite clear that Fred is in a spot of trouble. Fred will go out of business because he charges too much because his costs are too high; everyone is buying bread from Harry. Fred is what we call an inefficient supplier - it would be better for the economy if Fred went off and did something else productive instead... perhaps he should go milk some cows.
Now, Coles and Woolworths say "we're going to charge $4 for our bread". Suddenly Fred (having time-travelled from "the good ol' days" to the 21st century) finds that he can supply bread and, unlike before, make a profit. Coles and Woolworths might pay him $3.10 for each loaf of bread (so he makes 10c on each loaf), and they sell it for $4 (so they make 90c on each loaf). However, this doesn't change the fact that Fred is inefficient and should be milking cows instead. A Fred who's producing bread is still an inefficiency that is detrimental to the economy. This is the first point being made - the way companies have captured market power is bad for the economy because Fred gets to make bread, Woolworths and Coles get to sell it at $4, and consumers have no choice but to buy it.
Inflation is the idea of rising prices - you could buy way more with $1 in 1940 than you can with $1 today ("Back in my day, when I was a young whippersnapper, you could buy a bag of lollies the size of my fist for only 5 cents!"). The next bit is simply saying that by companies such as Coles and Woolworths charging higher prices, they cause inflation. And thus, by introducing price controls in economies where companies have market power dominance, you can control inflation. Price controls are where like... the government says you're only allowed to charge $X for particular goods. Also, you shouldn't try to control the price in efficient economies like the good ol' days marketplace scenario (this can cause a multitude of other economic problems that I won't delve into).
Lastly, he says that companies having dominance is not *all* bad, because US companies can head abroad to foreign countries, set up market power dominance there, make a huge profit => US economy benefits. However, it doesn't mention the other side to this coin - the US economy benefits, but the foreign country economies suffer.