A substance is soluble if it dissolves in water. Salts follow general rules, so you can predict whether a salt dissolves without learning each one separately.
All common sodium, potassium and ammonium salts are soluble. All nitrates are soluble. Common chlorides are soluble, except those of silver and lead. Common sulfates are soluble, except those of lead, barium and calcium.
Common carbonates and hydroxides are insoluble, except those of sodium, potassium and ammonium. For example, copper carbonate and magnesium hydroxide are insoluble, but sodium carbonate and potassium hydroxide are soluble. An insoluble compound appears as a solid when it forms in water.