Maturation is the programmed, internal settings that allow your body and mind do something at a given stage in cognitive and physical development, like the ability to walk when one is approx. one year old.
Object permanence is the stage at around 7mo old, when babies start to remember an object even when it is now hidden, and may reach to look at it, perhaps like a colorful bookshelf.
There are certain periods of time in one's development in which a particular growth or skill is easiest/crucial to learn, like learning to have reciprocal, developed language by age 8. After which learning is stunted.
Assimilation comes after an object has been introduced, and another idea which seems similar/the same is put in the same exact mental file, like a child seeing a football field and saying, "baseball field!"
Accommodation can come after assimilation. It is when an object is re-categorized into a new file to accommodate for a new idea, such as a "football field" in addition to a "baseball field".