An investment fund is a pool of money contributed by a small or large number of subscribers, unit-holders or shareholders, which is invested and administered on their behalf. In some jurisdictions, these functions have to be exercised by separate bodies, but in many, two or more can be combined. All three functions are rewarded with fees, usually based on the value of the fund, but sometimes being success-based.
Many countries have favourable tax regimes for mutual funds, to encourage saving.
As the name implies, investments are limited to those securities listed on public stock exchanges. One which has no pre-determined closing date. One with a pre-determined closing date, on which the fund's assets must be realised and the proceeds distributed back to the subscribers. Closed-end funds are normally used by groups of private investors, often working in 'limited partnerships' for tax reasons. Broadly speaking, this means that if you see an offshore fund being marketed in a high-tax country, its investment behaviour is probably quite constrained, and this may limit its ability to achieve high returns, in the interests of protecting investors.