A family of Microsoft relational database management systems designed for ease of use.
You are including a reference to the Forms collection in the expression but not giving a name for the form. But as in this case the form is that in which the control is situated, you don't need to reference the form at all, simply the control.
=DLookUp("[Abr]","Regions","[ID] = " & [Parent])
However, on the basis of your description I don't think this is what you want to do as you refer to the form's recordset having a Parent column, which would mean the form is bound to the Regions table. If my understanding is correct what you want is a bound combo box rather than an unbound text box, set up like this:
ControlSource: Parent
RowSource: SELECT ID, Abr FROM Regions ORDER BY Abr;
BoundColumn: 1
ColumnCount: 2
ColumnWidths: 0cm
If your units of measurement are imperial rather than metric Access will automatically convert the last one. The important thing is that the dimension is zero to hide the first column. The value of the combo box, and hence of the parent column to which it is bound, will be the numeric Parent value, but by hiding the ID column returned as the first column by the control's RowSource query, the value shown in the control will be the text Abr value corresponding to the ID value which matches the Parent value in the column in the current record.
Where you could use an unbound control would be in a form bound to a referencing table which has a foreign key column. RegionID say, referencing the ID column in the regions table, e.g. a table of locations within a region. This table would not have a Parent column of course as parent is determined by Region. However, the expression to call the Dlookup function would be like this:
=DLookUp("[Abr]","Regions","[ID] = " & DLookup(["Parent]","Regions", "[ID] = " & [RegionID]))
i.e. it looks up the Abr value from the row in Regions where the ID value equals the value of Parent in that row in regions with the ID value matching the foreign key RegionID selected in the current record in the form bound to the referencing table.
BTW I would advise against using parent as a column name as it is the name of a built in property in Acces, so should be avoided as an object name. ParentRegion would be better.