Accessioning an object or item is the action of officially adding it to a museum's collection.

When an object gets admitted to a museum's collection, it is recorded in the museum's register and given an accession number by which it can be identified in all future documentation and references.    

In Brazil

Accessioning is not understood in Brazil in the same way as in the English speaking countries. In the Brazilian context, accessioning is part of the acquistion process. That is, when an object is acquired, it is already officially considered part of the collection. Assigning a registration number happens shortly after the acquistion procedures are finalized, normally when the object is inscribed in the museum´s catalog or register.
Another interesting point to discuss and that may serve to illustrate even more the differences between the two contexts is that, in the English speaking countries, acquisition represents the moment when an object enters a museum, but its destination remains to be discussed (considering the fact that it may become part of the collection or will turn into something else as a handling collection/educational material). If the object is going to become part of the museum collection, it will be accessioned. But this is not a common or widespread practice in Brazil, the objects, when acquired, are usually exclusively for the museum´s collection.