Solventless describes concentrates made without chemical solvents like butane, propane, CO2 or ethanol. Instead, makers separate trichomes and oils using only physical methods: water, ice, sifting, heat and pressure.
The main solventless products are kief and dry sift (trichomes sifted through screens), ice-water or bubble hash (trichomes knocked off in ice water and filtered through mesh bags), rosin (oil pressed out of flower, kief or hash with heat and pressure), and live rosin (rosin pressed from ice-water hash made from fresh-frozen plants).
Note the difference between "solventless" and "solvent-free." A well-purged hydrocarbon extract may test with only trace solvent, but it is still solvent-based because solvents were used. Solventless means none were used at any point.
People choose solventless products for a few reasons: preference for a process without chemical solvents, and the rich flavor that careful hash-making and pressing can produce. Solventless products are often more expensive because they take more starting material and labor.
Solventless does not automatically mean better or cleaner; quality still depends on the starting material and the maker. A COA shows potency and screening for pesticides, microbes and more.