A liquidity premium is the extra return investors demand for holding a security that is less liquid. Liquidity premia explain a number of important aspects of securities prices including the size effect and the usual slope of the yield curve.
The reason for the existence of liquidity premia is simple. Suppose two securities exist, which are identical in terms of risk and return, but one is more liquid than the other (so it can be sold more quickly). Which would you rather hold?
Measuring the size of a liquidity premium is usually difficult. It can be hard to separate from other, usually larger, determinants of prices such as risk premia and expectations about future interest rates. A liquidity premium is also likely to vary over time, which further complicates estimation.
The lower liquidity of longer term government bonds is the commonest explanation of the usual (downward sloping) shape of the yield curve. The lower liquidity of small caps is, similarly, the most convincing current explanation of the size effect. However, this is less important because the persistence of the size effect over the long term and in different markets is less well established than the shape of the yield curve. There are plenty of exceptions to both.