A blue lightsaber is a color common to a "Jedi Guardian," one of the schools of the Jedi Order (yeah, they had different schools within the "Jedi" title, just ride with it) and those sabers represented that their wielders were more or less battle-ready. They'd focus on learning different lightsaber combat techniques and increasing their power in the skills needed by a warrior. Obi-Wan Kenobi and Anakin Skywalker both line up with that definition, and are good examples of the mindset of the Jedi Guardian.
The green lightsaber is usually found with the "Jedi Consulars," who are a bit more thoughtful with their approach to being a Jedi Knight. Instead of focusing on combat techniques, the Consular has a closer connection to the non-physical Force. These Jedi will, as much as possible, avoid using the Force to attack, and are forced into action typically only in defense of a Jedi ideal. Good examples are Yoda and Jedi Luke as he appears in Return of the Jedi.
The yellow lightsaber has only been glimpsed so far in novels and cartoons in canon, but they are the color of the "Jedi Sentinel," a type of Jedi that learns practical skills and seeks a more balanced view than the Consulars and the Guardians. The skills they learn are useful to them in their lives (like Rey's knack with electronics), not used primarily for combat, even though Jedi Sentinels are formidable fighters. They also aren't as close to the Force as a non-combat skill as Consulars.
In the Legends lore, Jedi Sentinels have been depicted as being some of the most complex Jedi. The Guardians of the Jedi Temple in Star Wars: The Clone Wars used double-bladed yellow lightsaber pikes to defend the Order's most sacred locations. Asajj Ventress, a Sith who turned to the light, finds a yellow-bladed lightsaber on the intergalactic black market and wields it once she's turned good. In canon, we haven't seen a yellow-bladed Master on screen before, so Rey Skywalker is our first.