What is the function of "Last import" in Address Book? I just made a synchronization through iTunes of my iPhone onto my MacBookPro.

From memory I made about ten modifications on my iPhone.
Unfortunately they are not in the relevant group, but within All Contacts.

I thought it will be natural to find them within the group Last Import.
But they aren't there.

Moreover, on a total number of entries of about 600, more than 500 of
them are within this Last Import group.

This is a huge problem: where I'm expecting 10 entries to place in the right group, I'm facing a list of more than 500.

What is the real usefull function of this Last Import group?
What may I did wrong to get such a huge Last Import.

I tried to simplify this huge problem by creating a New Smart Group… based on rule:

Card was updated after Aug 15th 2013


But this smart group is still abnormal:
73 cards where I'm expecting no more than 10.
Last Import is a group that is expected to contain contacts acquired when you use the File > Import menu item. Since you modified existing contacts on your iPhone, your MBP does not see these contacts as imported, just modified.

Your smart group creation sounds correct. It will locate any contact that has been modified by you or by another program, since the smart group rule is acting on the last modification date property of the person records. For example, if you use your iPhone to add a phone number to an existing contact, that contact has been modified indirectly (outside of the Contacts apps on OS X or iOS). Or if you send an email to a person, Mail might modify the record to change how the name or email address is displayed. Or when your contacts are synced through iCloud, there may be other non-visible changes to your contacts that force an update to the last modification date. So, unfortunately, a card was updated after (date) smart group does not strictly show you contacts that you edited directly, but instead it shows all modified contacts.

Having said all that, I don't have a better solution for you. I think you will need to use the card was updated after (date) smart group rule, and scan through that list of contacts to find the contacts of interest.