There was an article written by Beckley Mason on ESPN.com titled "The Book on Tom Thibodeau." It's an excellent article in which Mason delves a lot into Thibodeau's philosophy and system of play. You can read the entire article here. For now, here is a segment on his defensive principles:
Thibodeau’s defensive system is the pinnacle of team defensive strategy in the NBA. He is often credited with being the first coach to fully leverage the abolition of illegal defense by loading up the strong side box while having the weakside defenders zone the back side of the defense. In effect, Thibodeau's defenses force ball handlers -- whether in isolation or in side pick-and-rolls -- to the baseline and then send a second defender from the weakside over to the strong side block to cut off dribble penetration.
He is especially detail-oriented when it comes to pick-and-roll defense, getting down to the specific angles that each defender’s feet should be pointing. Thibodeau wants to send everything away from the middle of the court and force lob passes or bounce passes out to the perimeter, allowing defenders more time to get back to their men.
Off the ball, every defender in the Thibodeau system will have his hands up and active, with arms stretched as wide as possible. The goal isn’t actually to get deflections, though that happens. The real objective is to take away the first passing option of the offense -- to make the ball handler hesitate and throw a slow pass rather than whipping a chest pass to an open shooter. This gives the defense more time to recover from screens and cuts and often forces the ball away from the offense’s primary option on a given play.
Thibodeau knows he can't ask his defenders to do everything, rather he teaches them to take away certain high-percentage options for the offense. When everyone does their jobs, the odds tilt heavily in the defense's favor.
Most of Thibodeau’s offensive sets are not rudimentary, but he tends to keep things basic in big moments. It’s not uncommon to see some brilliant flex-based sets early in the game devolve into a steady diet of standard pick-and-rolls and pin-downs by the fourth quarter. He makes solid adjustments from game to game. For instance, he used Noah in the middle of the court to unlock Miami’s pick-and-roll defense in their 2011 playoff series, but Thibodeau is not known for drawing up brilliant offensive game plans on the fly.