Compression members are structural elements that are pushed together or carry a load, more technically they are subjected only to axial compressive forces. That is, the loads are applied on the longitudinal axis through the centroid of the member cross section, and the load over the cross sectional area gives the stress on the compressed member. In buildings posts and columns are almost always compression members as are the top chord of trusses.
The loading capacity of a short column is determined by strength limit of the material. The strength of a column of intermediate size is limited by its degree of inelasticity. A long column is constrained by the elastic limit (that is by amount of buckling).