A meta data value field or filter, is an element in a search, which works with meta data, eg
A meta data element is created using the "Meta data field" tab:
The data, which such an element works with is the item_metafield.value table and column. This can be changed using the Field.
Everything, except the data, which a filter or value field does work on, can be edited using the 3 The Details panel, i.e. the choice of meta data cannot be changed after creation.