what does the united nations commission on international trade law (uncitral) arbitration mean?

It means that the parties have chosen the UNCITRAL arbitration rules to apply to their arbitration. Other than the LCIA, ICC, ICDR, AAA or a number of arbitration courts and organizations, UNCITRAL does not itself administer arbitrations or get involved with individual cases.

why do some parties chose the uncitral arbitration rules and an ad hoc arbitration, rather than have an arbitration organization/institution (such as the lcia or icc) administer the arbitration?

Some parties believe that ad hoc arbitrations under the UNCITRAL rules are less expensive because the proceedings are administered by the arbitrators themselves rather than using the additional services (and costs) of an arbitral organization.

who is allowed to use the uncitral arbitration rules?

Any party may agree to use them irrespective of their nationality. Because they carry the imprimatur of the United Nations, and are not associated with any particular arbitration institution located in a particular country or part of the world, many parties regard a choice to apply the UNCITRAL rules as impartial and politically neutral.