I'll stast by explaining what a HCL is and how it works, and then move on to background correction.
A hollow cathode lamp (HCL) is a hollow glass tube filled with low pressure of some noble gas (Neon or Argon), inside the glass tube there is a cathode and an anode. The cathode is made with the metal you are interested in measuring.
The lamp works as follows: A potential difference is applied between the cathode and the anode, such that the cathode has a lower potential than the anode. The potential must be high enough to ionize part of the gas that fills the tube, the positively charged cations accelerate towards the cathode, while the electrons fly towards the anode. When the cations hit the cathode some of the metal atoms in its surface detach, afterwards, this detached atoms become excited due to collisions with nearby atoms and release this excitation energy as photons (light). The photons emitted are, in principle of different single specific wavelenghts depending on the energy difference between the excited and base states, however, there are some phenomena (mostly the fact that there are other nearby atoms that slightly shift the energy levels, and the Doppler effect) that contribute to the single wavelenghts being instead small intervals of wavelenght. This is called "Line Broadening". This line broadening is more apparent if there is a higher concentration of atoms in the vicinity of the emitting atom, or if temperature is higher.
If a higher potential difference is applied between the cathode and the anode, then a higher amount of atoms is emitted from the cathode, because cations impact the cathode with a higher kinetic energy. This high concentration of atoms means two things: First, its very likely that the emitted radiation will be reabsorbed by some nearby atoms, this has the effect of lowering the intensity of the "lines" emitted by the HCL. Second, a high concentration of atoms and higher temperature (atoms collide with higher kinetic energy, wich implies higher temperature) will mean that the lines will broaden considerably (a link to an image is provided at the end of the answer)
The Smith-Hieftje background correction works as follows: First the absorption by the sample of the lines emitted by the HCL is measured normally by the detector. This includes the absorption by the analyte and the background absortion due to matrix effects, etc. Then a pulse of high voltage is applied to the HCL, so that the emission lines are broadened and the center of the lines is self-absorbed by the atoms in the lamp as described previously.
Because the analyte can only absorb the wavelenght that was already self absorbed by the HCL, the analyte won't absorb anything. The matrix and other impurities, however, will absorb the wavelenghts of the broadened line (background absorption typically has the form of wide absortion bands, not single lines, so taking out a single frequency doesn't affect it much, think continuum background correction with deuterium lamps).
Now one has both, the value of the absortion of the analyte + background and of the background. The only thing left to do is substract them, which is done automatically. This process is repeated periodically, during the duration of the measurement (after the pulse of voltage is made, a small interval of time has to pass so that the detached metal atoms in the HCL can deposit themselves again in the surface of the HCL and don't interfere with subsequent measurements).
www.agilent.com/cs/library/applications/a-aa14.pdf (hollow cathode lamps)
https://books.google.com.ar/books?id=eTz6AwAAQBAJ&pg=PA478&lpg=PA478&dq=Smith-Hieftje+background+correction&source=bl&ots=Rst6iNgPM6&sig=2JOZBeSiYOutOOzSuZg2RNqSNls&hl=en&sa=X&ved=0ahUKEwizjPSi2Z3LAhXLh5AKHYL4Cn4Q6AEIUDAI#v=onepage&q=Smith-Hieftje%20background%20correction&f=false (a neat book, not specifically on AAS but has a nice explanation of background correction, check page 478 for an image of a self-absorbed, broadened emission line).