What is the joke behind "fork" and "spoon" keywords? Christina decides a keyword which will make her believe Hououin Kyouma's story in the next time-line. That password is:


  私が今一番欲しい物はMy-Forkであり。
  My-Spoonはもうもってるし。
  The thing I most want at the moment is "my fork".
  I already have "my spoon".


She blushes as soon as she says it. And when Kyouma repeats her this password in the following time-lines, she feels strongly ashamed (especially for the "spoon" thing) of it everytime.

What is the reason behind Christina's intense embarrassment?
According to an interview with the scenario writer, Naotaka Hayashi, featured in Dengeki Games Magazine about the heroines of anime/game that weren’t explained in the main story:

Why did Kurisu want her own fork?
Ever since Kurisu came back to Japan she couldn’t get enough of instant ramen. At first she tried using chopsticks to eat her ramen but never could get used to them, so she gave up and used a fork instead. This is why she wanted her own personal fork to eat her ramen at the lab.

This is probably the actual meaning she implies. Her comment about how Okabe shouldn't take an interest (i.e., ask more about it) in that, is probably something to hide he embarrassment of not being able to use chopsticks.
Note that she brought her own spoon for pudding, but she doesn't have a fork (for ramen).