Suppose I say that Sheila is good at math and you ask me why I think so and I offer this argument: "Sheila is good at math because she is a physics major." The inferential claim involved in this argument is inductive. I am only claiming that Shela's being a physics major makes it probable or likely that she is good at math. It is unlikely that I think that her majoring in physics makes it impossible for her to be bad at math. And, since in fact most physics majors are good at math, this inductive argument is strong. It is reasonable to suppose that Sheila is good at math from the premise that she is a physics major.
In contrast suppose I say "Frank is good at math. After all, he's Chinese." This is a weak inductive argument. The fact that Frank is Chinese offers little support for the conclusion.
Sometimes the arguments which people give have false premises. I might, for example, argue that Sheila is probably good at math and give as my reason that she is majoring in physics, when in fact I'm wrong about Sheila's major. In evaluating people's inductive arguments we look at two parts. We evaluate the inferential claim as strong or weak (or something in between) and we evaluate the truth of their premises. A good inductive argument will be both strong and have only true premises.
Inductive arguments are called cogent if they meet both these conditions: 1) the inference is strong and 2) none of the premises are false.