The liquidity premium refers to the additional return investors demand for holding a relatively less liquid asset. It's a concept mainly used in the bond world because markets tend to contain more similar assets, meaning you can better isolate the liquidity factor when comparing two assets. Still, it's also applicable in equity and other asset classes.

Why liquidity matters
To continue the analogy, consider that a highly desirable property came up on Island C, and investors in Island A and Island B wanted to buy it and finance the purchase by selling their existing property. Property owners on Island A could buy it quicker because they operate in a more liquid market, while property owners on Island B might need to cut their prices dramatically to get a quick sale.
The liquidity premium also applies to equities. For example, consider two companies operating in similar industries but with substantial liquidity differences in their shares.
During the financial crisis of 2008-2009, many investors faced pressure to fund losses elsewhere and sought to sell stocks to do so. Investors in the less-liquid equities would have had to discount the price heavily to complete a sale. As such, investors were willing to pay a higher valuation for the more liquid asset than the less liquid asset, all things being equal.