Enumerative induction, or induction, is a method used to draw a conclusion based on some supporting observed pattern.
For example, take the inductive inference, "Every cloud that I have observed has been white. Therefore, all clouds must be white." This inference is using some observed pattern, namely, that all the clouds the observer has seen have been white, to draw some larger conclusion that all clouds must be white. Notably, induction doesn't need to draw a true conclusion – it is simply a method of reasoning that is used to draw some conclusion. You could easily draw a false conclusion through induction, like, "every cat I have observed has been black. Therefore, all cats must be black." Perhaps this observer has only seen black cats in their life, but clearly, this does not mean that all cats must be black!
Philosophically, induction is an interesting construct. We use induction all the time in our daily lives, yet logically speaking, we do not have certainty that our inductive practices will be true. Despite this, when making arguments, we use induction and commonly accept such arguments as reasonable. Without induction, of course, it would hard to be make progress living our lives. After all, induction is, in a sense, the way that we make predictions about the future! We take some observed pattern from the past and apply it to draw a conclusion about what future events hold. At the same time, however, induction does present a logical problem when trying to construct robust, philosophical arguments, as will be highlighted in the below section.
The primary way that induction is utilized in debate is to prove that consequentialist frameworks are inherently unverifiable. As mentioned in the previous paragraph, we use induction when making a prediction about the future. We draw upon some previous, past experience and use that to draw a conclusion about what will happen going forward. This, however, is the problem; we are simply making a prediction about the future, but we have no certainty about what will happen in the future.
Debaters will argue that "induction fails," which is taken to mean that the process of induction itself is circular. The argument goes, we know that past events can be used to predict future events. However, we only know this because in the past, past events have been shown to predict future events. Therefore, we have no way of knowing that in the present, past events will continue being able to predict future events. So, any framework that relies on predicting future events fail.
While this argument might sound silly at first, induction is an issue taken seriously in philosophy. To be certain of the conclusion of any argument, we must be certain that the conclusion will always hold to be true; it isn't enough to simply have a very high degree of confidence in the truth of the argument. Even a utilitarian framework, for instance, doesn't say it is moral to maximize predicted pleasure and minimize predicted pain; instead, it says it is moral to maximize actual pleasure and minimize actual pain. However, the only way to do this would require knowing an exact account of the future, which induction cannot provide.