density
Density is how much mass is packed into a given volume - how heavy a material is for its size. It answers 'why does a small lead fishing weight feel heavier than a big loaf of bread?' Formally, density (the Greek letter rho) equals mass divided by volume: rho = m/V. The usual unit is grams per cubic centimeter (g/cm^3), or kilograms per cubic meter.
Some numbers to anchor it. Water is 1.0 g/cm^3 by definition. Polymers are around 0.9 to 1.4 (they roughly float or barely sink). Aluminum is 2.7, titanium 4.5, steel about 7.9, copper 8.9, lead 11.3, gold 19.3. Ceramics sit around 2 to 6. So a steel part is nearly three times heavier than the same-sized aluminum part, and gold is about 19 times heavier than water. Density comes from two things: how heavy the individual atoms are, and how tightly they pack (their crystal structure and packing factor).
Engineers care about density because it is often the enemy in design. For anything that moves or flies - a car, an aircraft, a phone - every gram costs fuel or performance, so engineers chase a high strength-to-weight or stiffness-to-weight ratio (strength divided by density). That is why aluminum, titanium, and carbon-fiber composites win in aerospace even though steel is cheaper and sometimes stronger in absolute terms. Density also drives whether things float, and shipping and handling costs.
A bicycle frame in steel might weigh 2.5 kg; the same design in aluminum (about one-third the density) weighs roughly 1.3 kg, and in carbon-fiber composite (lighter still) under 1 kg. Same shape, very different mass - density in action.
Why lightweight design chases low density.
Low density does not mean weak, and high density does not mean strong - they are independent properties. Lead is dense but soft; carbon fiber is light yet very strong. In weight-critical design what matters is the ratio of strength or stiffness to density, not either one alone.