Points to consider when reading this book:
First, it is a book about logic and not about science. It was written nearly 80 years ago in response to the questions raised when the mechanistic Newtonian universe was seemingly turned upside down by the introduction of quantum mechanics, and in particular this is a response to the propagation of Heisenberg's uncertainty principle. The question it addresses is: of what does our scientific knowledge logically consist? Note the key word, "logically."
Popper basically makes two arguments. One is that there is no inductive logic leading to scientific hypotheses. Again, note the word "logic." This does not mean that in formulating hypotheses scientists do not reason backwards from experience. Of course they do. We all know the famous examples of Newton's apple and Einstein's clock tower. What Popper means to point out is that there are no formal logical rules that govern such reasoning. In other words, there is nothing inherent in the apple that must of necessity lead to the laws of gravity, and nothing inherent in the clock tower that must of necessity lead to the theory of relativity. So why call it inductive logic? Better, argues Popper, to call it "psychologism." In other words, we don't really know what was going on in Newton's or Einstein's mind, but we do know that it was not formal logic.
His second argument is that scientific hypotheses can not be proved to be logically true. Again, note the word "logically." Logically, all we can do is falsify them, and that the wider the field of falsification is, the better they can be "corroborated." (Assuming, of course, that they are in fact not falsified). And that it is this "corroboration" that is the closest we can get to proof. In other words, a hypothesis can never be proved, only disproved, and that in the strictly logical sense, a hypothesis can never make a prediction about a singular occurrence, (much as we can not say that a six will necessarily show up on our first six rolls of the dice). Again, this does not mean that in the real world we do not or can not make scientific predictions. Indeed, if we did not, we would have no computers, no satellites, no automobiles, not much of anything really. It's just that in an infinite world, with an infinite number of occurrences, there is no way to logically - there's that magic word again - prove that in at least one case the scientific theories we use to underpin such technology will not fail.
Of course, Popper is a much deeper thinker than I am, and his arguments more profound, but that's the essence of it the way I see it, and so I guess it's up to you as to whether you are willing to read several hundred pages of this type of thinking. I was. If nothing else, it's good exercise for the brain.
Note: I just wanted to add that if you find yourself getting lost as you plow through this text -- I did myself more times than I care to admit -- don't give up but keep plodding ahead. Eventually you'll come back to familiar ground. And if all else fails, Popper does a very nice job of summing everything up in the final chapters.