A biochip is effectively a small piece of glass with small dots of
DNA on it. Say we do this for a human. You can extract DNA from a human
cell and dot it onto the biochip. You can then extract
RNA from a cell and label it with a
fluorescent marker. The RNA will bind to the DNA on the chip if it matches, so you're left with a bunch of DNA with some bits of RNA attached. Now for the cool part. Since the RNA is fluorescent, you can see which bits bound. This tells you which bits of DNA are expressed in the cell you got the RNA from (DNA makes RNA, for those of you who remember the
central dogma). So you can now pick out all the bits that code for things in that cell.
This isn't the most interesting bit, though. Now go and do the same thing for another cell. Now compare the two. Any differences will be caused by different expression of the DNA. If one bit of DNA is expressed in one cell and not another, it probably corresponds to a gene that is important to the function of one cell and not another. If you compare a tumor cell to a healthy one, you can see the genes that are responsible for the cancer. If you compare a skin cell to a nerve one, you can see which proteins are required for each.
At the moment, this is generating large amounts of data and very little useful information. The software to cope with it isn't really there yet. Get in there now and be as famous as Eugene Myers.