Yeah, it would help a lot if you've played through the first one.
BIG SPOILERS FOR THOSE OF YOU WHO MAY HAVE ACCIDENTALLY WANDERED IN HERE.
I'll do these in a basic chronological order.
-Harry Mason and wife find a baby on the side of the road in/around Silent Hill, adopt her, and name her Cheryl.
-Several years later, Harry's wife dies from an illness.
-Several more years later, Cheryl convinces Harry to take her to Silent Hill for a vacation. During the ride there, a girl suddenly appears (Alessa) and causes Harry to crash the car.
-He wakes up to find Cheryl missing. He travels all around Silent Hill uncovering a plot by Dahlia Gillespie to birth a god.
-Basically, Dahlia used her own daughter (Alessa) to birth the god and during her whole painful, mess of a childhood, Alessa "separated" herself in half and created Cheryl preventing the god from being born at that time. Cheryl was "brought" back to Alessa. (
A lot more to this story)
-Anyways, Harry kills the god produced by Dahlia's second attempt, and before dying Alessa/Cheryl hands Harry an infant (another form) later to be named Heather.
-So SH3 takes place 17 years after the original, and Claudia (Alessa's childhood friend and fellow cult member) wants to again try giving birth to a god through Heather/Alessa/Cheryl.
I think that's about it. I'm writing this at 5:30 a.m. so forgive for any mistakes I may have made. For a
much better, in-depth analysis, try reading the Plot Guide
here at GameFaqs. I highly recommend that you do. After re-reading what I typed even I'm confused.