Bottom space is a psychological state in which one person submits his or her will to another. Many submissives are not people who "go around bottoming to the world". They need to undergo a certain degree of mental shift before they can really submit to another person; this is often called "entering bottom space". (There is, of course, a symmetrical concept of top space.)
This tends to be more a term used in domination and submission than in more physically oriented BDSM play. That is, this is not so much about things like a warm-up spanking before taking heavier pain: this is about letting go of ego.
Many people who are not 24/7 players ritualise entering a submissive state. For example, a bottom might be expected to strip naked, to put on a collar or allow a collar to be placed on them, to kneel in a particular way, or even to answer to a different name as part of a ritual of entering bottom space. Repetition of such acts over repeated sessions strongly associates the acts with a shift of mental state.
Nakedness, a collar or a "slave name" are all mild examples of humiliation, which is often a major component of entering bottom space. A somewhat more psychologically intense technique with a similar dymamic is to combine erotic stimulation with verbal humiliation. For example, a dominant partner might slowly masturbate his or her sub (usually short of orgasm, especially if the sub is male) while saying things that in another context might be mildly insulting, or stopping often and making the sub beg for continuation… or for anything else the dominant partner tells the sub to beg for!