This is meant in two distinct senses: static replication, where the portfolio has the same cash flows as the reference asset (and no changes need to be made to maintain this), and dynamic replication, where the portfolio does not have the same cash flows, but has the same "Greeks" as the reference asset, meaning that for small (properly, infinitesimal) changes to underlying market parameters, the price of the asset and the price of the portfolio change in the same way.
Further, dynamic replication is invariably imperfect, since actual price movements are not infinitesimal – they may in fact be large – and transaction costs to change the hedge are not zero.
In the valuation of a life insurance company, the actuary considers a series of future uncertain cashflows (including incoming premiums and outgoing claims, for example) and attempts to put a value on these cashflows.
Such a construction, which requires only fixed-income securities, is even possible for participating contracts (at least when bonuses are based on the performance of the backing assets).
[1] Advantages of a static replicating portfolio approach include: Valuing options and guarantees can require complex nested stochastic calculations.