If you think of a rocket taking off we use the expression to 'blast off'. So to 'blast through' means to go through something with a great deal of force/strength Best wishes Bob

Literally, "to blast through" suggests using dynamite or explosives to remove a barrier--a rocky hill, or perhaps a concrete wall. In the case of prices, sometimes there will seem to be price levels that are like psychological barriers. Perhaps house prices gradually rose, to €70.000 and €80.000 and €90.000, but seemed to stop rising as they approached €100.000. That level seemed like some kind of limit. People would look at a €100.000 price and refuse to pay. Then, suddenly, prices rose, not just a little bit above €100.000, but a lot. And they didn't fall back, they kept on climbing. It is as if prices had encountered a concrete wall, and then "blasted through it" with explosives.

It means the average house price has increased very quickly over €100,000 and people are living longer.

It means that the prices not only went up till the 100.000 mark but they even got higher than that mark really fast. So they went up and passed the mark of 100.000 really fast, like an explosion or something. It is kind of a metaphor.