"Pressing Down the Pillow" means not letting your opponent's head up. In the Way of Martial Arts combat, it is wrong to let your opponent lead you around or push you into a defensive position.
-- Miyamoto Musashi, The Book of Five Rings
Some chess players use a similar idea when they play white, using bold openings they have memorized to crush black's development immediately, putting pressure on the king's bishop pawn right away, sometimes introducing the queen within the first few moves hoping black will start giving away pieces and/or open up the king.
This is gambling and either way is not likely going to make for a good match. When someone wields these memorized openings without understanding them well, even a less experienced player can upset them. Your opponent might well wiggle out of the trap and you will find yourself overextended, your pieces cornered in black's territory with no backup.
The end position above (white resigned at this point) came about when the player, an online opponent from Greece, used a bold variation on an opening attack on my king's bishop pawn (which, you will see, is still on the board). For a little while, he had suppressed my development and laid down a net fraught with dangerous sacrifices for me. I wasn't sure how this would turn out, so I just very calmly addressed the threats, developed the pieces as I could, taking my time. This is how it ended up: white overwhelmed, wondering how this happened.
I wonder how many games I've won as black merely because white came on too strong in the opening and didn't know what to do when the initial attack failed. Another tip from Musashi: time is infectious.
Being drawn in is something common to all things. Becoming sleepy is infectious, just as yawns and such are infectious. Time, too, is infectious. ... When your opponents show themselves to be skittish and hurried, you should give an appearance of being not at all affected by this, and rather move all the more leisurely. Your opponents will then be caught up by your actions and will show signs of slackening.
A tip about chess: unless you're a highly experienced player who has attained some mastery in position and theory, don't bother memorizing openings. For all the years I've played chess, I still don't really know Alekhine from alkaline. I've played hundreds if not thousands of games, and slowly I have come to a better understanding of the hidden cause and effect, of the strengths and weaknesses of a position as it changes move by move. It's hard to develop this understanding if you play nothing but speed chess.