New orchid growers, especially those beginning with phalaenopsis, sometimes get concerned with the “silvery-gray, squiggly things” that overhang the sides of the flower pot. (I once ran into someone who thought they were flower spikes and had staked them vertically.) In fact, those are roots, specifically “aerial roots”, so named because they tend to project into the air, rather than growing down into the medium.
Like any other roots, they function primarily to absorb water and nutrients. In some plants, they also contain chlorophyll so can contribute to the photosynthesis processes of the plant. For that reason it is advisable not to remove them and to wet them thoroughly whenever you water the plant.
In the wild, the aerial roots may also serve as “guy wires”, giving the plant mechanical stability against gravity and wind storms that may attempt to rip the plants out of their host trees, much as guy wires are used on antenna towers.. That may not be so important for home-grown plants, but they may still function that way to some extent. For example, a phalaenopsis grown in a small pot will often have an extensive array of aerial roots. Transplant it into a much larger pot (not advisable unless you’re using an inert medium that wicks moisture uniformly), and those formerly-aerial roots will tend to sink themselves into the medium, and no additional aerial roots are grown.