Weightlessness (also referred to as microgravity or informally as zero gravity, zero g, or null gravity), is a condition experienced by objects in orbit, in free fall, or far from gravity sources, where the effects of gravity on motion are negligible.
In the real world, the terms "microgravity" and "weightlessness" are standard and "zero gravity" avoided because it is misleading. In Trek, like most science fiction, "zero gravity" is the term most commonly used.
In some species, including humans, long-term effects, if untreated, are loss of muscle mass and bone density. Short-term effects can include nausea and discomfort caused by redistribution of body fluids in to the head.
In some 7% of Andorians, swelling of the nasal passages can cause asphyxiation; this was prevented by inserting a grommets deep in the nasal cavity of all space-faring Andorians. (TOSS #14 "Zero G")
Most species experienced prolonged weightlessness only after developing space travel. Operating in weightless conditions requires training and can have adverse effects on health, so most advanced civilisations used artificial gravity in space stations and vessels and gravity boots during extravehicular activity.
As late as the 23rd century, some equipment designed before artificial gravity was common required a microgravity environment. (TOSS #30 "Bactry Anecdote")
There may also be accidental zero-g anomalies caused by overlapping artificial gravity fields. (ENT: "Broken Bow", TOS novel Enterprise: The First Adventure)