No, she didn't go to the White House; the actual country of Turkey.
The visit has various geopolitical ramifications: Turkey's been pledging the EU for years, and a little hospitality like this plays well on the world stage. Also, given how many Turkish guest workers there are in the Netherlands, and with a rising tide of violence both in and from these (mostly Muslim) communities, it doesn't hurt the Hague to play nice either.
Here's what the Turkish Daily News had to say; if you so choose, you can chase it with a little something from DutchNews.
PS: Her Majesty's birthday was on 30 January; a belated Happy Birthday Ma'am.