A trustee is an entity that controls and administers the trust property. This can be either a natural person or a corporation charged with the duty of being the 'trustee'.
A trustee maintains legal title over the trust property but not beneficial title. As such the property is held in the entity's capacity as trustee and not in their own right.
The trustee is most likely to be appointed by the trust instrument/deed, though a trustee can be granted powers by statute or by the court.
The duties of a trustee are very important and serious. In many cases they will be investing or protecting the trust assets on behalf of the beneficiaries. The trustee owes the beneficiaries fiduciary obligations. Essentially, the trustee cannot unduly profit from the relationship nor create a situation of conflict between the trustee's or external interests and the interests of the beneficiaries. The trustee must also ensure that trust assets, particularly monies, are kept separate to their own personal assets. For example, the trustee should not use the same bank account for their own private and trust funds as this would cause them to become mixed.
A trustee can also be a beneficiary, however they cannot be the sole trustee and beneficiary, for then they would already hold legal and equitable title, meaning there is no need for the trust to exist at all.