Inductive reasoning takes specific observations and makes general conclusions out of them. It is often contrasted with deductive reasoning, which takes general premises and moves to a specific conclusion. Both forms are useful in various ways. The basic strength of inductive reasoning is its use in predicting what might happen in the future or in establishing the possibility of what you will encounter. The main weakness of inductive reasoning is that it is incomplete, and you may reach false conclusions even with accurate observations.
Inductive reasoning takes specific observations and draws general conclusions from those observations. You may look at 100 dogs, for instance, and find that they all have fleas and then declare that all dogs have fleas. The problem, obviously, is that you have not examined all dogs, so as soon as one is found without fleas, your conclusion is proven wrong. What you can determine is that it is likely that a dog will have fleas because all dogs you have come into contact with have them. The more observations you make will determine how accurate your conclusion is.
The strength of inductive reasoning lies in establishing probability. You might observe that when it is very cloudy there is rain. Pure inductive reasoning would say that means it will rain on all cloudy days. You will observe days when this is not true, but through inductive reasoning you establish the probability that it could rain on a cloudy day and prepare accordingly.
Another strength is that inductive reasoning allows you to be wrong. It is only through more observation that you determine whether your premises are true. Detectives use this method of reasoning when investigating a crime. They see patterns or make observations that lead them to certain conclusions. That sets their path in motion, and they will either prove their conclusion right or wrong with further investigation. The value is that this form of reasoning has at least given them some direction.
The greatest weakness of inductive reasoning is that it is limited. In the dog analogy, once you see a dog without fleas, your conclusion that all dogs have fleas is proven incorrect. Another problem comes when your observations are incorrect. If you have only seen large dogs, you might conclude that all dogs are large. The reasoning is sound, but incorrect because the observation was incomplete or incorrect. If you stop with just a few observations and do not continue to investigate, your conclusion will not be valid no matter how firmly you believe it. Your logic can be sound but proven incorrect by further observation.
Using Inductive Reasoning
Inductive reasoning is used all the time in many ways. In the cloudy day example above, you use inductive reasoning to say because it often rains on cloudy days, it is likely that you will encounter rain, so you take whatever steps you need to with that knowledge. There remains the possibility of no rain, so it is not necessary that the conclusion be absolutely correct in all cases. You may also use inductive reasoning to help investigate or search for truth.