Can a person control their brain's electrical activity? In a brain-computer interface paper, I found the following paragraph: 


  Effective assessment of BCI performance requires two levels of evaluation: the user and the system. The user must control the signal features ..."


My question is how can a person control the signal features of his/her brain signal? Does this mean, for example, that a person can give more attention to increase signal to noise ratio for the P300 signal, and be able to look more carefully at the screen that shows flashes in an SSVEP experiment?
Yes, and no.  Biofeedback has been an active field of research since the 70s, but has been a bit "fringified" as a cure for ADHD, etc.  

It is possible to fine tune the brain activity for specific tasks.  To borrow an example from BCI, the Rolandic Mu Rhythm can be used to "train" a user to refine the movement of a cursor or other pointing device.

Jonathan Wolpaw has been doing BCI work long before it was "cool", so his work on BCIs for ALS patients is definitely worth checking out. 

As to whether you could train the P300, this signal is seen most prevalently in the "oddball" paradigm, which by nature relies on the stimulus that evokes it being of low probability. Letting the user know that a low probability stimulus is about to occur would eliminate most of the response.