We have discussed this before but it bears repeating that bitcoin is a major technical achievement. It is the first practical success at creating a decentralized trusted asset ledger. This will have implications far beyond ‘currency’. If you are new to this, start with the following:
General Context 1 [updated Jan 22, 2014]
Marc Andreessen's op-ed in the New York Times of why bitcoin matters. Best single intro article to bitcoin I think
http://dealbook.nytimes.com/2014/01/21/why-bitcoin-matters/?_php=true&_type=blogs&_r=0
General Context 2
Good context setting if you read the quick 4 part blog series.
http://www.circle.com/2013/10/30/circle-bitcoin-global-digital-currency/
By Jeremy Allaire (formerly CEO Brightcove, Macromedia)
Bitcoin as a Platform/Protocol
http://www.usv.com/posts/bitcoin-as-protocol
By Albert Wenger (partner, Union Square Ventures)
http://startupboy.com/2013/11/07/bitcoin-the-internet-of-money/
By Naval Ravikant (Founder, Angellist)
Excellent Description of "Mining"
http://qz.com/154877/by-reading-this-page-you-are-mining-bitcoins/Applications of Bitcoin
About as clear and non-technical as it can be made. I love the characterization of mining as competitive bookkeeping.
Broader Applications of BTC
http://www.finextra.com/video/video.aspx?videoid=513
Interview with Richard Brown (executive architect, IBM)
12:29 minutes
Once you have done that and are ready to understand more, watch this Khan Academy series. You will need to watch some episodes more than once but once you do you will have a grasp of the technical basics.
For the full bitcoin series: ledracapital.com/bitcoin
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