What is "trading for liquidity reasons"?

It means that the insiders are selling because they want cash.

This paragraph on page 1 makes the reasoning clearer:

Another unique aspect of insiders is that they often receive a large proportion of their stakes in firms through non-market transactions (e.g. stock grants). Through initial ownership, stock grants, and other market transactions, insiders firm stockholdings are often a non-trivial percentage of their wealth. Thus personal liquidity and diversification motives, in addition to signaling and regulatory issues, will affect the timing and nature of insider trades, making it more difficult for price setters to interpret any given insider trade as informative or not.

It says that insiders are relatively cash-poor. Insiders sell their shares because they need cash.