Being a trustee means looking after other people's assets (even though you might be a beneficiary yourself there will be other beneficiaries and you are looking after the trust's assets for them as well). You need to think of caring for the assets in a way that is at least as good as, or better than you would look after your own assets.
As a trustee of a family Trust, you must look after the assets, invest them properly and make distributions. You must do this as a "Prudent Person" would do it.
Think about this like borrowing a friend's car. You might not keep your own car very tidy nor always check the oil and water as often as you should. But when you are borrowing a friend's car chances are you will take special care of it and give it back tidy and in good condition. You are in a position of trust with the friend's car and you will not want to breach that trust.
Some of the management tasks the trustees must perform are:
Owning assets as trustee puts greater onus on you than if you owned them just for yourself. Many people forming a trust appoint a professional as trustee who will make sure that the management of the trust is properly done.