As an aspiring medical professional (finishing a doctoral degree in physical therapy), I like to think that I have at least slightly more knowledge of athletics and their involved injuries than the typical layman. It definitely shows my inner geek that I can watch the replay and discern what injury a player has incurred with reasonable success. Let me use that knowledge to better inform you.
I'm not going to prattle on to you about anatomy and physiology, in general or specific to the knee. If you are dying to know, you can use Google to your heart's content.
The basics are that your knee has three types of ligaments; the cruciate ligaments (anterior and posterior) that form the "X" in the center of your knee capsule, the collateral ligaments (medial and lateral) around the outsides, and the meniscus in the middle that allows the knee to bend without moving bone on bone.
Each of those ligaments protects against severe forces in the direction opposite its name - aka, Joaquim's MCL (medial collateral ligament) protects him from severe forces from a lateral direction. Or, at least, that's the goal - provide a sudden enough and strong enough force, and even the best support structure will give way.
This most likely occurs during what some like to call "loaded motion" - a joint experiencing force in more than one direction at the same time. MCL tears typically occur when a blow is dealt to the outside of the knee while the foot is planted on the ground.
In this instance, Joaquim had a teammate roll into his knee while his foot was planted on the court. However, Vander was lucky - athletes know all about the O'Donoghue triad, when a lateral blow to the knee very often results in tearing the ACL, the MCL, and the lateral meniscus.
An isolated MCL tear means that likely the force imparted on Joaquim's knee wasn't very large (relatively speaking), and it also means a great deal of luck - an isolated MCL tear very rarely requires surgery and can be rehabbed with relative ease.
Here's a little more FYI for you to view:
The goal is essentially to strengthen everything else in the leg and provide the athlete with optimal control going forward. The 4-6 week timeline is for his entire recovery from "injured" to "playing", believe it or not. Joaquim will likely spend a week or two using a brace that prevents any side-to-side motion of the knee, and will only have that knee moved and strengthened while he is in his physical therapy sessions.
By strengthening both his hip and all the muscles that function to bend and straighten his knee, the goal is to have control of the knee such that he will not find himself in any side-to-side deviation of his knee. He essentially will be without that ligament for the rest of his life, so he'll have to work harder to avoid those lateral forces without the protective structure in place.
By the time the Warriors begin their season on November 9th against Maryland-Eastern Shore (which happens to be exactly six weeks from the date of the injury), Joaquim should be back to full strength or close to it, with the last question or hangup being his lateral mobility.
This is usually the last thing to return, the ability to plant and cut quickly, but it is also less of a concern for him as a big man (not exactly known for his lateral quickness).
However, he may continue to play with at least a neoprene sleeve on the knee as a means of assisting him with the future pursuit of avoiding the loaded motion that got him in trouble to begin with.