inducible refers to able to be made “on demand” – typically used to describe a gene expression system in which you can get a gene transcribed and/or translated by adding or removing a chemical. “Inducing” something is basically doing the thing you need to do to “switch it on.” This allows you to control the expression of the gene which can be helpful for restricting its expression to certain cell types and/or times. A common place this comes up in biochemistry is with using IPTG to induce the expression of genes controlled by the lac operon in bacteria. See the post on bacterial protein overexpression for more.