In baseball, the pitcher throws pitches to the batter. Each pitch not hit into play is deemed either a ball or a strike. A ball is a pitch where the batter does not swing, yet the pitch is outside of the strike zone – in other words, the pitch is either too high or too low, or else not over the plate.
Three strikes and the batter is out, but four balls and the batter is awarded a walk, also known as a base on balls. A walk is considered good for the hitting team, and not good for the team in the field.
When the count is 3-0 (that is, when the batter has three balls, and no strikes), it is considered good strategy to take the next pitch (that is, to let it go by, without swinging at it). The reason is simple: if this pitch is outside the strike zone, you get awarded a free base. If it's in the strike zone, though, you still have a favorable count, 3-1. So, during most pitches, the batter stands tense, ready to make the a split-second decision: Swing? Or take the pitch? However, when the count is 3-0, quite often, the batters have no intention of swinging at the ball. The batter will stand much more relaxed, and calmly watch the pitch go by.
So, the simile in your passage simply refers to someone being relaxed and still, unlikely to move or flinch.
If you'd like to watch an example, have a look at this video. It starts with the batter having a 3-0 count. He obviously has no intention of taking swing at the next pitch, which is called a strike. (In this case, the batter doesn't agree – he was ready to take his walk – but the umpire gets to make the determination, not the batter.) In the next two pitches, the batter's stance and posture are completely different from how it looked in the fourth pitch.
The phrase is not a common one, but the game situation is. Therefore, the analogy is readily understandable to anyone familiar with the game of baseball, but it wouldn't be easy to figure out without that background knowledge.