Abe is one of the first characters we meet. We're told in the first paragraph that he "lived in an orphanage, fought in wars, crossed oceans […] performed in circuses, knew everything about guns and self-defense and surviving in the wilderness, and spoke at least three languages that weren't English" (Prologue.1). So yeah, he was a busy man, and kind of sounds like the ultimate grandpa. Don't you want him to tell you a bedtime story?
Unfortunately, most of his family thinks he made all this stuff up. He may be an amazing grandpa to Jacob, but he wasn't a good father. Jacob's dad even thinks that his own father was a dirty cheater, going on "business" trips that were more "bizness" than business, if you catch our drift.
Abe is discouraged when Jacob stops believing his fantastic tales. Maybe he's used to it, because his own son stopped believing in him long ago. Either way, though, he dies with no one believing in him, killed by the hands (well, tentacles) of the very monsters that he was trying to get them to believe in. Which is pretty depressing.
Jacob's journey is as much about learning to believe as it is about redeeming Grandpa's character. He slowly learns that everything Grandpa talked about was true—the monsters, the peculiar children, the magical orphanage—and Emma calls Abe "one of the most honorable men I have ever known" (11.147). So maybe Jacob's dad has misjudged the guy, too.
By the end of the book, Jacob knows that Grandpa was a great man after all. Emma leaves Jacob's dad a note about how wonderful he is, too, so we hope Dad gets the memo.