In The Logic of Scientific Discovery, sec. 85, Popper writes:
Science is not a system of certain, or well-established, statements; nor is it a system which steadily advances towards a state of finality. Our science is not knowledge (epistēmē): it can never claim to have attained truth, or even a substitute for it, such as probability.
Yet science has more than mere biological survival value. It is not only a useful instrument. Although it can attain neither truth nor probability, the striving for knowledge and the search for truth are still the strongest motives of scientific discovery.
What does Popper mean when he denies science is "knowledge (epistēmē)"? He explains (sec. 85):
The old scientific ideal of epistēmē—of absolutely certain, demonstrable knowledge—has proved to be an idol. The demand for scientific objectivity makes it inevitable that every scientific statement must remain tentative for ever.
His point here is fallibility. There's no way to ever prove an idea with finality so that there's no possibility of it ever being overthrown or improved in the future. There's no way to be 100% certain that a new criticism won't be invented later.
People consider Popper a skeptic because they see the options as infallibilism or skepticism. Popper does deny infallibilist conceptions of knowledge, but disagrees that infallibilism is a requirement of genuine knowledge.
In the first quote, Popper uses the word "knowledge" in two different senses, which is confusing. The first use is qualified as "epistēmē" and refers to view that we must find a way around fallibility or we don't have any knowledge. The second use, in "striving for knowledge", means good ideas (useful ideas, ideas which solve problems) as opposed to random, arbitrary or worthless ideas. The view that we have no way to judge some ideas as better than others is the skeptical position; in contrast, Popper says we can use criticism to differentiate ideas.
I'll now discuss individual pieces of the first quote.
[science] can never claim to have attained truth
Popper means that even if we had an idea with no errors, we have no means to absolutely prove it has no errors and then claim there are none. There are no methods which guarantee the elimination of all errors from any set of ideas.
An idea with no errors can be called a final or perfect truth. It can't be refuted. It also can't be improved. It's an end of progress. Human knowledge, by contrast, is an infinite journey in which we make progress but don't reach a final end point at which thinking stops.
Could there be unbounded progress while some ideas, e.g. 2+2=4, are never revisited? Yes but there's nothing to gain by being dogmatic, and there're no arguments which yield exceptions to fallibility. Just accept all ideas are potentially open to criticism, and then focus your research on areas you consider promising or find problematic. And if someone has a surprising insight contradicting something you were confident of, refute it rather than dismissing it.
[science] can attain neither truth nor probability
Regarding probability: There's no way to measure how close to the (perfect) truth an idea is, how much error it contains, or how likely it is to be (perfectly) true. The method of judging ideas by (primarily informal) critical arguments doesn't allow for establishing ideas as probable, and the alternative epistemological methods don't work (Popper has criticisms of them, including on logical grounds).
Also, probability applies to physical events (e.g. probability of a die rolling a 6), not to ideas. An idea either is (perfectly) true or it isn't. Probability of ideas is a metaphor for positive support or justification. I've addressed that issue under the heading: gradations of certainty.
Science is not a system of certain, or well-established, statements
What's good about scientific statements if they aren't well-established or certain? They aren't refuted. We've looked, but haven't found any errors in them. That's better than ideas which are refuted. I shouldn't accept or act on ideas when I'm aware of (relevant) errors in them.
My judgements are capable of being mistaken in general. But that isn't a criticism of any particular judgement. Ideas should be rejected due to critical arguments, not due to fallibility itself.
striving for knowledge and the search for truth
The human capacity for error ruins some projects (e.g. attaining absolute certainty, attaining epistēmē). But it doesn't prevent us from creating a succession of better and better ideas by finding and fixing some of our errors.