In Freud's early work, he considered that neuroses in adults were attributable to sexual abuse when those adults were children. Those children repressed these memories as a way of protecting their "selves" and also in order to feel and appear to others what was considered "normal." Freud later supposed that not all neuroses were the result of abuse. He did however continue to argue that neurotics and so called normal people all use forms of repression for similar ends: to repress strange or troubling desires/fears in order to protect the self (by not dwelling on them) and also to conform to what society deems "normal."
To illustrate how this worked, Freud used the terms id, ego and superego. The id represents the instinctual desires, the ego is the realistic function which seeks to manage the id's desires in the real world in realistic ways and the superego is the moral or parental function. These are not parts of the brain; they are functions of the conscious/unconscious workings. Certain desires from the id are not socially acceptable, so the ego tries to make them manifest in realistic ways. If they are immoral (i.e. adultery), the superego manifests guilt to dissuade the self from indulging in such a desire. In some cases, the desire is repressed (buried in the unconscious). Thus, a kind of self-censorship occurs; some desires are managed by the ego and some are repressed. This mechanism of repression is conscious at times, unconscious at others.
Freud's famous method for baring (uncovering) these hidden desires was the "talking cure." He would get the patient to talk about dreams and would use free word associations. What has become known as the "Freudian slip," today usually refers to a situation where someone involuntarily makes a sexual reference - usually out of context. The Freudian slip or "parapraxis" is not necessarily sexual. The idea is that such slips may reveal some repressed desire or some remnant of a traumatic or significant event in the patient's life. And of course, sometimes the slip turns out to be insignificant.
Freud's work with dreams also shows how this censorship (repression) works. We have "dream thoughts" which are unfulfilled wishes or desires. Through a process called "dream work" we unconsciously repress these thoughts by translating them and condensing them into the manifest "dream content." Like Freud used the talking cure, the surface level dream content would be analyzed to uncover what had been condensed or left out. "Dreams (manifest surface dream content) are brief, meagre and laconic in comparison with the range and wealth of the dream-thoughts" (Interpretation of Dreams). As bizarre as dreams can be, Freud sought to uncover more hidden (and perhaps more bizarre) meanings.
To put it even more simply, the unconscious repression Freud talks about is similar to conscious repression we do every day. Freud is known for investigating sexual desires, psychoses, and deviant desires, but also the function of repression in general. So, something may be unconsciously repressed for a myriad of reasons. A person may consciously repress a desire (calling his/her boss a - insert bad word -) because the consequences outweigh the satisfaction one might get from indulging in such a desire. Although Freud dealt mostly with the unconscious, repression is also a conscious function.