It allows asset managers to capture the efficiencies of larger pools of assets (see economics of scale) although fashioning investment funds to separate market niches.
[1] Sometimes, especially when the feeders are hedge funds, this is a way of complying with the legal systems of distinct jurisdictions.
For a U.S. taxable investor, the ownership of shares in what is known as a "passive foreign investment company" or PFIC can prove to be very tax-expensive.
The offshore feeder fund almost always meets the definition of a PFIC.
An (onshore) master fund does not, so the transaction is set up so that the master fund is a partnership for U.S. tax purposes, which effectively provides insulation between the US based investor and the PFIC feeder.