A Market Neutral Fund seeks 0 beta. What this means is that in any given environment the fund should have limited exposure to market moves. (It makes money purely on alpha by getting the pairs trade right)
When equities rally strongly traders like to ride this trend. Usually this means following the beta of the trade. However, if you have a market neutral strategy you wont be getting that beta, so your returns will not be as strong as say taking an underlying position in a US ETF or S&P 500 futures contract.
The concept of equitising is just that - you are an investor, the market is rallying and you want ‘more return’ which you are not getting in your Market Neutral Fund, so you ‘index the equity’ which is the same thing as buying the equity index through a futures contract or ETF.
Your result now is a market neutral fund which is showing low correlation to the equity markets AND you are also getting equity like returns because you have overlaid a long futures position in that market so you can get some beta exposure.