In a disability context, “institution” means something like “an organization that keeps disabled folks separate from mainstream society and under the control of others”.
It used to be fairly common practice for families (under great pressure from doctors and state authorities) to send their disabled children to residential institutions and then have no further relationship with them. That’s fallen out of favor in the past couple of decades, but a lot of the underlying power dynamics remain in service providers in other settings.
For instance, group homes are often referred to as being “living in the community” rather than “institutions”, but they also often have identical power dynamics.
Similarly, some places will say that they are not institutions but are rather “intentional communities” or some sort of utopian village because they are farms and cottages rather than big harshly lit buildings. But again, they have the same power dynamics.
The power dynamics can be hard to spot if you don’t know how to look for them, because a lot of institutions will go out of their way to pretend they’re doing something fundamentally different.