When you have a Trust as part of your estate plan, you have to choose someone to be a "Trustee". The Trustee is the person (or people) who have to follow the instructions in the Trust and do what is says. Depending on what type of Trust you have, you might be your own Trustee, or, you might have chosen someone else to be a Trustee. Trust administration refers to the actions taken by the Trustee, to do what the Trust instructs them to do.
The Trustee must keep strict compliance with the terms of Trust, as well as compliance with the applicable state and federal law. While a Trustee is generally allowed to charge a reasonable fee for the services provided, the job does come with some potential pitfalls. For example, beneficiaries might not be happy with the Trust investments, sale of property, and/or feeling like they aren't getting their "fair share".