I will go about this by answering two questions. First, what is Popper's general approach when attempting to distinguish science from pseudo-science? Second, what specifically did he dislike about Freudian psychoanalysis? (Historically, Popper actually developed his general theory in response to his particular dislike of contemporary marxism and Adlerian and Freudian Psychoanalysis.)

Falsificationism

Popper proposes that in the empirical domain, nothing can ever be proved true. No swans are black because you've never seen a black swan, and you've seen thousands of swans? Well, maybe the next swan you'll see is black. This may be unlikely, but not impossible, and thus, there is no proof. (The general problem is the problem of induction, as discussed by Hume, which leads into an infinite regress.)

Thus, science is not what is proved true. Science is also not what can explain a lot of observed phenomena, because telling stories about the past is easy and always open. Instead, Popper proposes science is that which contains the means of its own refutation. Everything may be wrong, and a quality of the good ways of exploring the world is that they make clear how to see if they could be wrong. Thus, good science

• makes bold conjectures about how the world is like, that is, claims the world is in a state which would be surprising unless the theory were true

• derives from this predictions of what should never be the outcome of experiments

• would appears as false - falsified - if those outcomes were in fact to turn up

Thus, something that is never false is unscientific, and if it claims to be science, it is pseudo-science. That which could easily be shown false, but has so far withstood many genuine attempts at falsifying it can be scientific.

A few notes: Popper did not claim that anything that is not falsifiable is bad, or false. Something may be true and unfalsifiable, and it may be good and unfalsifiable. But to claim the status of being scientific, it needs to be falsifiable.

Psychoanalysis

Popper used to be a fan of psychoanalysis, especially of the Adlerian brand influential in Vienna in that time. His friends, he observed, were especially impressed by the ability of Adlerians to explain any and all phenomena. A man is honest? It's this kind of early-childhood event that caused this. A man is dishonest? It's that kind of early-childhood event. The Adlerians were never wrong. And it was not clear how they could ever be wrong, as they could post-hoc tell a story about how any given phenomenon fit their theories perfectly. Everything in the world was to them evidence for their theory.

This eventually came to appear to Popper as deeply misguided. Adler himself, with whom Popper worked, was exclusively telling stories about how the past proved or confirmed his theory, never claiming how a possible future state of events could disprove it. He had no predictions, and thus, no truly scientific experiments.

This made Popper not only give up on psychoanalysis, but led him to use it as one primary example of what he considered pseudo-science.

The same story also applies to Freudian psychoanalysis; between all the different complexes and drives, every possible human action or mindset could be explained as originating from childhood experiences and conflicting unconscious mental agents. But Freudians did not make bold conjectures, and did not attempt to falsify their theory with truly scientific experiments.

Sources

Popper lays this out in SCIENCE: CONJECTURES AND REFUTATIONS, in the 1st chapter. It is a great read and accessibly written.

Although Popper's own words are probably the best explanation on this (as they are so clear here), it probably won't hurt to skim by the Stanford Encyclopedia for a secondary source.