Inflation is when prices of things rise as time goes on. For example, a new Mercedes-Benz C-class that costs $38,000 today may cost over $45,000 in a few years due to rising prices. If you buy a pack of gum for a dollar today, it will be a lot higher in 20 years from now.
Due to the inflation of prices for products, the dollar is becoming more and more useless every day, just like the "45 cents" in your question. What can you buy with 45 cents? Nothing. This quote is saying that as time goes on, there is less use for the dollar.
There was actually a time when quarter dollars were useful. Back in the 1960's, you could actually pay for a gallon of gas for one dollar. Now, here in the United States where I live, it's about $3.30 per gallon (and that's CHEAP compared to the rest of the United States).
So, to put it simply, the dollar in our time is becoming less useful, and is almost useless now.