A line around which a body or geometric figure actually or mentally revolves. In a more general sense – a line around or parallel to which something is moving or could be found. In elementary school, we learn that there is a mental axis around which the Earth revolves, this imaginary line helps to understand how the Earth revolves around itself and the Sun at the same time.
In semiotics, the distinguishing features of syntagmatic and paradigmatic (associative) relationships are often depicted as located around two different axes.
Syntagmatic relations arise between the sets of signifiers in a given sentence; they are part of linear, temporal sequences in which one signifier heard at that moment replaces another that has just been heard, and in turn, is replaced by another that is yet to be heard.
It is assumed that this sequence moves around a horizontal axis. Relationships, usually depicted as inhabiting the space around a vertical axis, Ferdinand de Saussure called associative, today the term paradigmatic is more common. These are relationships between signifiers that have been used and those that could be used instead of the former.
These relationships do not happen in time, at any moment they form a rainbow of possibilities that frames and accompanies the currently used signifiers.
Just as we imagine the Earth to revolve around an imaginary axis, it would be useful to think of sentences as moving (located) around two different, intersecting axes.