Though Holmes often speaks of deduction, his famed power of drawing conclusions from minute details is a form of induction.
The conclusion of a deductive argument contains no information beyond what is contained in the premises. Or, more formally, if the premises of a deductive argument are true, then the conclusion cannot be false. Here's an example.
Everyone puts Baby somewhere.
No places are corners.
Therefore nobody puts Baby in a corner.
This is a deductive argument—a syllogism, to be precise. If (1) and (2) are true, then it is impossible for (3) not to be true.
By contrast, inductive arguments contain new information—that is, their conclusions go beyond what is contained in their premises. The premises of an inductive argument make the conclusion more likely, though that conclusion could still be false.
Most of science proceeds via induction. We conclude things like PV=nRT because we measure the pressure, volume, temperature and molarity of gasses over and over and find that this pattern holds, so long as you don't make it really cold, put the gas under huge pressure, or start with an especially heavy gas. In other words, PV=nRT is true under all but the most exceptional circumstances.
Induction makes a conclusion likely to be true, but it doesn't guarantee it.
If you've watched an episode of House, then you sort of already know this. Every episode includes at least one wrong diagnosis—one likely, but ultimately erroneous conclusion derived from keen observations, before that final moment of insight, helpfully illustrated with a clever metaphor.
Bell was a (real) Scottish physician who practiced in the late Victorian era. And Bell was himself famous for his inductive reasoning—specifically, his ability to draw conclusions about things like people's hometown, current residence and profession by observing details such as accents, the color of mud on their boots and their calluses. On several occasions, Bell deployed his reasoning skills to assist in police investigations, becoming one of the early pioneers of forensic science.