You have a few problems which I'd like to point out, and I hope you can learn something from them. Here we go...

Memory management

When you create an object using alloc, new, or copy, such as [[NSArray alloc] ...] or [[NSString alloc] ...], it is returned with a +1 retained count. This means you "own" the object and are responsible for releasing it later by calling release (which you're not currently doing in your code). If you use, for example, [NSArray arrayWith...], then you don't get a +1 retain count (you get an autoreleased object), and if you want it to stick around you have to call retain.

That said, when you do

NSMutableArray *newArray = [[[NSMutableArray alloc] initWithCapacity:4] retain];

The alloc gives you a +1 retain count, and then you're calling retain a second time! This is unnecessary.

However, since you don't need to use your arrays or strings outside this function, you don't need to retain them at all, so you can just use:

NSMutableArray *newArray = [NSMutableArray arrayWithCapacity:4];

and

NSString *val = [NSString stringWithString:[existingSection2 objectAtIndex:i]];
// or even more simply
NSString *val = [existingSection2 objectAtIndex:i];

For more details and best practices, please read the Memory Management Programming Guide.

Loops/iteration

Your method of using [existingSection2 count] and i++ in a for loop works, but isn't the best way to do things. Obj-C has what's called Fast Enumeration, which is a lot simpler and I hope you'll use it:

for (NSString *val in existingSection2) {
    //...
}

NSLog and format strings

The NSLog function works (similar to C's printf) by taking a format string (which contains format specifiers like %d for integers and %@ for Obj-C objects), and then a list of arguments to put in for the specifiers.

When you use

NSLog(@"new array description: ",[newArray description]);

you will only log the string "new array description: " because you don't have a format specifier corresponding to the description. Instead you should do:

NSLog(@"new array description: %@", [newArray description]);
// or even more simply
NSLog(@"new array description: %@", newArray);

There's also more information available on the String Format Specifiers that you can use with NSLog.

Overall

Here's a rewrite of your code using the techniques I described above.

NSMutableArray *newArray = [NSMutableArray arrayWithCapacity:4];
NSArray *existingSection2 = [NSArray arrayWithObjects:@"S2 Item1",@"S2 Item2",@"S2 Item3",@"S2 Item4",nil];

for (NSString *val in existingSection2) {
    [newArray addObject:val];
    NSLog(@"value is %@",val);
    NSLog(@"new array contains: %@", newArray);
}
NSLog(@"what's in newArray: %@",[newArray objectAtIndex:0]);

you have a logging problem:

NSLog(@"new array description: ",[newArray description]);

should be

NSLog(@"new array description: %@",[newArray description]);

bonus help:

NSMutableArray *newArray = [[NSMutableArray alloc] initWithCapacity:4];  // fix memory leak
NSArray *existingSection2 = [[NSArray alloc] initWithObjects:@"S2 Item1",@"S2 Item2",@"S2 Item3",@"S2 Item4",nil];

for (id section in existingSection2) // fast enumeration
{
    NSString *val = [[NSString alloc] initWithString:[existingSection2 objectAtIndex:i]];
    [newArray addObject:val];
    NSLog(@"val %i is %@ new array now contains: %@",i,val,[newArray objectAtIndex:i]);
    NSLog(@"new array description: %@",[newArray description]);
    [val release]; // fix memory leak
}

NSLog(@"what's in newArray: %@",[newArray objectAtIndex:0]);