Dovish vs Hawkish: This refers to how accommodative the Fed's policy stance might be.  Have you ever seen a hawk stare down its prey?  That's how a hawkish Fed looks at inflation (i.e. "I'm really close to swooping in and killing that!").  Doves, on the other hand--well... I don't know what doves do, but I know they're not hawkish!

When it came to today's FOMC announcement, the Fed had a chance to send a clear signal on their rate hike intentions (if they had any).  While they did dial up the hawkishness just a bit, they stopped short of the sort of overt telegraph seen in last October's meeting (when they said "in considering whether it will be appropriate to raise [rates] at its next meeting").  

As such, markets (led by word-parsing computer programs) spent the first few seconds reacting to the more hawkish parts of the statement.  The Fed thinks the economy is doing better?  Sell bonds!  But when the clear telegraph was nowhere to be found, human decision makers said "no... BUY bonds!"  And buy they did.  10yr yields traded all the way down to 1.50 and Fannie 3.0s added nearly 3/8ths of a point versus yesterday's latest levels.