Mechanism of induction by IPTG
The gene coding for T7 RNA polymerase itself has been engineered into many commercially available E. coli strains under a modified lac operon system. You'll often see this called DE3 in the name of the E. coli strain i.e. BL21(DE3) cells. Instead of a T7 promoter sequence in front of the lac operator sequence, there is a lac promoter sequence that native E. coli RNA polymerase is able to bind. As soon as the lac repressor protein (LacI) falls of the lac operator sequence of DNA in the host chromosome, T7 RNA polymerase will be transcribed and translated. Some strains of E. coli add an additional gene coding for T7 lysozyme which inactivates the T7 promoter i.e. strains like BL21(DE3)pLysS. This keeps background expression levels of T7 RNA polymerase from expressing your protein prior to induction.