In the simplest terms, the principle of sufficient reason (PSR) states that everything that exists has a sufficient explanation/reason/cause/grounding (there are different variations of the PSR, e.g. Contrastive PSR) for its existence.
In Moreh Nevukhim 1:72, Rambam says that he thinks that there are many things that simply exist for no purpose and have no good explanation for why they should exist (this is also the passage where Rambam rejects G-d's total involvement in the world):
Again, in the body of each individual there are parts which are intended for a certain purpose, as the organs of nutrition for the preservation of the individual, the organs of generation for the preservation of the species, the hands and eyes for administering to certain wants, as to food, etc.: there are also parts which, in themselves, are not intended for any purpose, but are mere accessories and adjuncts to the constitution of the other parts. The peculiar constitution of the organs, indispensable for the conservation of their particular forms and for the performance of their primary functions, produces, whilst it serves its special purpose, according to the nature of the substance, other things, such as the hair and the complexion of the body. Being mere accessories, they are not formed according to a fixed rule: some are altogether absent in many individuals; and vary considerably in others. This is not the case with the organs of the body. You never find that the liver of one person is ten times larger than that of another person, but you may find a person without a beard, or without hair on certain parts of his body, or with a beard ten times longer than that of another man. Instances of this phenomenon, viz., great variation as regards hair and colour, are not rare. The same differences occur in the constitution of the Universe. Some species exist as an integral part of the whole system: these are constant and follow a fixed law; though they vary as far as their nature permits, this variation is insignificant in quantity and quality. Other species do not serve any purpose: they are the mere result of the general nature of transient things, as, e.g., the various insects which are generated in dunghills, the animals generated in rotten fruit, or in fetid liquids, and worms generated in the intestines, etc. In short, everything devoid of the power of generation belongs to this class. You will, therefore, find that these things do not follow a fixed law, although their entire absence is just as impossible as the absence of different complexions and of different kinds of hair amongst human beings.
However, in other places, Rambam seems to presuppose PSR in one of his proofs for the existence of G-d, blessed be He, which has been summarized by Rabbi Assaf Bednarsh goes like this:
The Rambam presents a slightly different version of the cosmological argument, which is valid even if one were to postulate the eternity of the universe. He argues that all movement must be caused by some force, and therefore, since there is movement in the universe, there must be some prime mover who moves the highest sphere, which then moves the lower spheres, and ultimately the physical objects in our world. That prime mover is God. [Mishneh Torah, Hilkhot Yesodei Ha-Torah 1:5; Moreh Nevukhim 2:1]
So it's not quite clear to me whether Rambam affirms (in some form) or rejects PSR? Does he ever state anything like that explicitly or perhaps I'm just misunderstanding the Moreh Nevukhim 1:72?