The term middleman refers to a party that provides an intermediary service in a transaction. Middlemen normally charge a fee when providing their service, as is the case with trusts.
In finance, a middleman is typically a broker that holds shares on behalf of their clients. For example, the unit shares of a widely held fixed investment trust are normally held by a broker that is acting in the role of a middleman. In exchange for providing this service, the broker / middleman may collect a commission when the shares are sold and charge a fee to maintain the account.
When a process is deemed economically inefficient, it might be suggested to "cut out the middleman." For example, retailers oftentimes act as middleman between manufacturers and consumers. Eliminating the role of the middleman / retailer should ultimately lower the cost to the consumer.