Plot and structure are similar but very different at the same time. Both have a vital role to play in a work of fiction.
Basically, plot is what happens, structure is how you tell the reader about it.
Plot is linear. Structure isn't, or doesn't have to be. Structure should be chosen to reinforce plot. In other words you decide how to tell your story (structure) to get maximum impact from the sequence of events (plot).
Because structure is non linear you can use devices like flashbacks to tell your story out of order. This is very handy if you want to shoot the sheriff on the first page but you have a lot leading up to the shooting that the reader has to understand.
Structure also involves such things as viewpoint (who's telling the story). Different viewpoints have different effects on the impact on the reader. Viewpoint is an important way of controlling the pace of your story. By intercutting scenes from different plot threads you can build excitement, fill in background the hero may not know, and move your story along.
For a good example of this see Tom Clancy's Red Storm Rising, an alternate history account of a Soviet invasion of Europe. Clancy's story spreads from Iceland to Moscow and he cuts back and forth between the characters (usually on chapter boundaries) to build suspense and keep the story rolling in spite of the amount of background material involved. James Clavell also made excellent use of shifting viewpoints in Shogun a novel of feudal Japan. The technique is especially helpful in long books -- which both "Red Storm" and "Shogun" are.
First person ("I did this...") is generally the most powerful, but the hardest to do throughout an entire work because you're limited to what your character knows at the time. That's why it is often mixed with either multiple first persons (hard to keep straight for the reader sometime), or first person and third person where the main part of the story is told through the protagonist's eyes and the supporting material, such as what other characters do when the protagonist isn't present.
Structure deserves careful consideration when you're plotting (actually plotting and structuring) your fiction, especially novels.