My theory for what happened on that Halloween night when Harry was a baby relies pretty heavily on this. It also has a lot to do with Wiccan beliefs and Sabbats, especially Samhain/Halloween. The Wiccan calender is called a wheel, and the year is divided into the dark half of the year and the light half of the year. On Samhain, which is technically November 1st, but the Wiccan days begin and end at sundown rather than at midnight as ours do, they are honoring their dead, it is a night when the veil between the world of the living and the world of the dead is at it's thinest, and actually sort of exists outside of time. It is also the night when the the Dark Lord (not an evil character in Wiccan lore, simply the aspect of the God when the nights are longer than the days) passes into the Underworld (dies) in order to implant himself as the seed to be reborn at Yule (Christmas to Christians) as the Child of Light, or the Sun King. The Dark Lord is the same being, who has three aspects or phases, Child of Light when he is first born at Yule, when the days start to get longer, but he is still weak as a child/infant, who grows in strength until he becomes the Sun King and reaches the peak of his power around June 21 (around the time of year when Voldemort tried to get Harry again, as in books 1,3, and 4) and then the next day he begins to lose strength and becomes the Dark Lord, finally dying and implanting himself into the body of a baby to be reincarnated at Yule. I think that it's possible that what he was trying to do on Halloween when Harry was a baby (and succeeded at least a little) was to put his sould and his powers into Harry so he would be reincarnated. Harry's parents of course didn't want their baby to be possessed by Voldemort and were trying to prevent it, so he killed them to get to Harry, which was probably why he didn't set out to kill Lily, but did when she was trying to keep him away from Harry.
Lily's wand was excellent for charms as Ollivander said in book one, and it seems that most protective spells are charms, like the Expelliarmus, and the Fidalius charm, not to mention that Flitwick was a dueling champion to back this logic up. So the way that Harry's mother saved Harry was that she put a very old, protective charm on Harry that caused Voldemort's plan to fail, allowing him to give Harry some of his power, but not allowing him to push out Harry's soul and replace it with his own. If he had succeeded in pushing out Harry's soul, then Harry would have died, but given Voldemort extra strength, the way Ginny was dying in the Chamber while Tom Riddle was growing stronger. Incidentally, while he was doing this and using Ginny to regain his power, this would be how she was able to speak parsletongue to call the snake. And the reason he is still trying to kill Harry is that in order for him to return to full power and to grow even stronger, Harry has to die; the process is that he puts his power and a bit of his sould into the new person, then takes it back and stealing their sould at the same time that he kills them. So Snape is afraid of Harry since he knows that was what Voldemort had in mind, and since CoS confirmed he had put some of his powers into Harry, he doesn't like or trust Harry, but at the same time, he *really* doesn't want Harry to die because then Voldemort would come back even more powerful and be pissed at Snape for spying.
As my daughter also pointed out, in book four, Voldemort is in the form of a baby, or resembles a very small, but deformed weird baby after he has started to try coming back but is too far from his full strength.."

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