If an illness or an injury is treatable, doctors can do something about it — medicine, an operation, therapy. The word lives almost entirely in medical talk, and it is usually said to calm someone down: "It's serious, but it's treatable." Notice what that sentence quietly means. Treatable is not the same as curable. Curable means the illness can be made to go away completely. Treatable means it can be handled, slowed, made smaller, made livable — the person can go on with life, sometimes with medicine forever. Many long illnesses are treatable and not curable, and doctors choose the word carefully for exactly that reason. So it is a hopeful word, but it is honest hope, not a promise. You attach it to the illness, not to the person: 'a treatable cancer', 'a treatable infection' — not 'he is treatable'. Outside medicine you will sometimes hear it stretched to problems in general ('a treatable problem'), but that sounds a little clinical, as if the problem were a patient. The opposite is 'untreatable', which is a heavy word — doctors do not say it lightly.