The reason why Obama and Hillary won Centre County is because of the influence of Penn State's University Park Campus there.
I can't find exit polls in PA to corroborate this versus W's 53-42% win in that county. I know that nationally, 18-24 split in 2000 but in 2004 they had shifted to Kerry by 9 points. But Bush won the county twice; in 2000, 53-42% and 2004, 51-47%. Admittedly the margin shrunk from 9 to 4 points in 4 years... though Santorum carried it 62-34% in 2000.
Obama swept it by 12 points in 2008, then won it 1 point in 2012, then Hillary won it by 2 points in 2016. For the record the township data does say that in 2016, the state college borough voted by 65-27% Clinton. But nationally, in both 2008 and 2012, young voters swung to the Democrats by wide margins.
Are we sure that this is the reason? This county has undergone definitely a transition from being a reliably Republican county to a Democratic county with about 75,000 votes cast.
Remember that in places with major colleges/universities, the decisive voting bloc is not the college-aged students (who, in many cases, have their votes count toward their hometowns, not their college towns), but the professors, lecturers, and other staff who work in these universities. These people are pretty much all highly educated, and thus tend to vote for left-leaning candidates.
In the case of Centre County, people who live in and around State College tend to vote Democratic, while people in the outer rural areas tend to vote Republican. Aside from Obama and Hillary, this county also voted for Bill Clinton in 1992 and 1996. Note that Bush won college-educated voters overall in 2000 and 2004, which is probably why he managed to win this county during his elections.