How Do Chips Make Credit Cards More Secure?

If you live in the United States, you might have recently gotten a credit card with a microchip on it. But what does this chip do that makes it any different than the magnetic strip on the back of the card?
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Sources:
http://www.zdnet.com/article/the-pin-debate-retailers-banks-divided-on-post-emv-card-security/
https://www.nbcnews.com/business/consumer/one-year-are-chip-cards-effective-or-just-very-annoying-n663851
http://www.omaha.com/money/the-sound-is-annoying-but-chip-reader-s-alert-helps/article_a7ebbf88-3caf-50cd-a189-58f7fd386fe1.html
https://beta.theglobeandmail.com/report-on-business/international-business/shift-to-chip-credit-cards-brings-us-in-line-with-canada-and-europe/article26590985/
https://www.theguardian.com/commentisfree/2014/jan/27/target-credit-card-breach-chip-pin-technology-europe
http://blog.credit.com/2014/09/what-your-credit-card-number-means-94136/
http://www.investopedia.com/terms/m/magnetic-stripe-card.asp
http://blog.opensecurityresearch.com/2012/02/deconstructing-credit-cards-data.html
https://motherboard.vice.com/en_us/article/mgbm7p/why-chip-credit-cards-are-more-secure-than-magnetic-stripes
https://www.creditcards.com/credit-card-news/emv-faq-chip-cards-answers-1264.php
https://quickbooks.intuit.com/r/emv-migration/how-do-emv-transactions-differ-from-magnetic-stripe-transactions/
https://security.stackexchange.com/questions/49234/why-are-chips-safer-than-magnetic-stripes
http://www.bankrate.com/finance/credit-cards/will-tokenization-protect-against-card-fraud.aspx
https://www.computerworld.com/article/2960791/financial-it/faq-what-you-need-to-know-about-chip-embedded-credit-cards.html
http://mashable.com/2015/10/01/emv-chip-credit-card-migration/
http://mashable.com/2015/11/11/consumers-credit-card-tokenization/
http://www.smartcardalliance.org/smart-cards-faq/
https://www.cryptomathic.com/hubfs/docs/cryptomathic_white_paper-emv_key_management.pdf [PDF]
http://www.secuilibrium.com/news/emv-how-does-the-crypto-work-in-chip-based-payment-cards
https://crypto.stanford.edu/~dabo/courses/cs255_winter14/lectures/EMV.pdf [PDF]