Q:

What did the gifts signify? 

Spoilers Ahead
In the movie "The Gift" what exactly did the gifts from Gordon signify?  Were those gifts somehow related to the past? 
Why exactly did Gordon show up every time at Simon's house? 

A:

The only gift that really had any significance in the movie was the final one.  All the other gifts were simply used to create foreshadowing and add mystery and suspense to the film as well as paint Gordon as a creepy, unstable person. 
Beyond that the only other purpose any of the other gifts or visits would have had is to allow Gordon to prepare for his ultimate plan.  The Apocalypse Now DVD was a little strange but I believe it was meant as foreshadowing as well.  And the visits to the house allowed him to get a copy of the key and gain Robyn's trust.