It refers to elements having 18 electrons instead of just 8 in their outermost electron configuration when they lose or gain electrons.
For example, Ag has 47 electrons when it's neutral: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s1 4d10
When it loses its 5s1 electron, it has an electron configuration of: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 4d10
notice that the highest energy level is 4s2 4p6 4d10 which has 18 electrons. Instead of saying it has a noble gas electron configuration like the s2 p6 octet it has s2 p6 d10 which is a "pseudo-noble gas electron configuration.
Therefore any element that has an outermost electron configuration of s2 p6 d10 instead of s2 p6 is known to have a pseudo-noble gas electron configuration.