The word 'induction' is unfortunately used in several different senses and invites confusion. It used to be common to use it refer to a kind of simple extrapolation, such as moving from all the ravens I've ever seen are black therefore all ravens are (probably) black. This might be called enumerative induction.
Sometimes induction is used to describe any argument whose conclusion is uncertain. This is unhelpful because at least sometimes an argument may proceed from uncertain premises to an uncertain conclusion in a way that is deductive. Some theorists call such reasoning probabilistic-deductive rather than inductive.
Sometimes induction is used broadly to mean any non-deductive form of inference, while often it is distinguished from abduction, which is usually understood to mean inference to the best explanation. C S Peirce distinguished between explicative reasoning, which draws out the consequences of what is already known, and ampliative reasoning, which provides cogent reasons for accepting a conclusion that is not entailed by its premises. Inductive and abductive inferences are both ampliative, in that their conclusions are not entailed by their premises and so 'go beyond' them.
Consider an example: suppose we entertain the proposition "the defendant is guilty of the murder of which he is charged". Now suppose we have some evidence for this: "the defendant's fingerprints (and no others) were found on the murder weapon". If we think of the evidence as a premise in an argument and the verdict as the conclusion, the premise does not entail the conclusion, but it does render it more plausible. If we add more evidence, e.g. "the defendant was seen arguing with the victim and was heard threatening to kill him", "the defendant was seen fleeing the scene of the murder covered in blood", "video footage shows the defendant repeatedly stabbing the victim", etc., then we have a highly compelling argument for accepting the conclusion. If we allow ourselves to use the language of probability, we might reasonably say that the premises render the conclusion probable. But no matter how much evidence we pile up, the premises will never entail the conclusion - even video footage can be faked. Nor is it simply a question of eliminating alternatives, despite Sherlock Holmes' famous dictum. The conclusion does not entail the premises either: the defendant could have murdered his victim without leaving his fingerprints behind. Eventually the jury must decide whether they believe the conclusion is true, or at least probable, and bring in a verdict, and whatever decision they make 'goes beyond' the data presented in the evidence.
In general the cogency of ampliative reasoning depends on all kinds of considerations, assumptions and background knowledge, which makes it difficult to give a general account of it. Attempts at finding a purely formal account of induction, e.g. by Rudolf Carnap, are widely considered to have failed. But statistical and algorithmic methods are still highly relevant to the issue of establishing whether some hypothesis is plausible on the strength of observed data.