You are talking about the mechanic's "feel" for materials. An experienced mechanic knows the elasticity of different materials and can feel when they are tight. For example if he was tightening a nut made from porcelain onto a bolt he would know to stop as soon as it was snug as any tighter would break the brittle porcelain. Tightening a steel nut onto a steel bolt he knows the difference between hand snug, tight and extremely tight where the metal is being stretched. He would also know instinctively when the limit was reached with brass, mild steel, hard steel and stainless steel and how much compression a washer can take although there are very many different alloys of steel so a torque wrench is always a good precaution especially, as others have written, when tightening multiple fasteners.
Personally I enjoy torquing up bolts using a torque wrench, the click as it goes over the top and the feeling that you're doing a proper job and taking time to do it right, is part of the joy of mechanical fettling.