There are certain areas within Importacular where the fields are not marked as green (required) fields i.e. required for data entry by Raiser's Edge, but they must not be blank for the data to import successfully. See this knowledgebase article for a full list of these key fields.
One example of this is Attributes. When creating a mapping for Attributes (within the Constituent area), the Category field is marked as required, however, the Description field must have a value (either it needs to be mapped to a field in the source or given a default value). If the Description field is not mapped and left blank, no error message will be displayed at the validation stage but the attribute will not be imported.
The same principle applies to Phone/Email mappings (there must always be a value in the Phone Number field).
The reason for this is that your data source may leave some fields blank and instead of importing a blank value you would want Importacular to ignore that mapping. For example, constituents that you are importing may have a mobile phone, but not always. In which case you could map the mobile phone type as a default but if the field in the data source is blank, you would not be adding a blank mobile phone entry in RE.
If all of your fields are populated, you should also check the respective Area Settings to determine if a selection there is preventing the data from importing (ie - if you selected an option to not import in the case of a match, etc.).