OK, so the front end of the car is on jack stands. The rear is planted on the ground. The car is in park.
Yet, I’m able to spin the front wheels with my hand.
Wouldn’t putting it in park lock the wheels via the transmission?
Yes it does. If you’ll notice, when you spin one wheel the other one spins in the opposite direction. There’s no way for that to happen when both wheels are on the ground, so the car can’t roll when it’s in park.
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It spins in the oppposite direction!!?? That’s wild! I never knew that!
I hate to be Captain Obvious, but…Are we talking about a car with FWD or one with RWD?
If your car has RWD, then it is perfectly normal for the front wheels to be able to spin when you jack up the front end of the car.
What is the make and model of the car in question?
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Um, without knowing he year, make, model, tranny, and 2WD or 4WD if that’s optional, how can we answer?
It it’s RWD, the front wheels are free to turn.
If it’s a FWD with a manual transmission, the wheel you turn will spin the ring gear (sometimes called a “crown gear” 'cause it looks kind of like a crown), which will turn the opposing wheel in the opposite direction. If it’s in neutral, you can even spin one wheel without turning the other. The axle will simply turn the spider gears, which will turn the pinion but since the “neutral” gear selection allows the tranny input shaft to spin independently of the tranny input shaft, the whole thing can spin without turning the engine or opposing wheel. The carrier for the differential gears actually spins, turning the “side gears” operate in a planetary manner, orbiting the ring gear. I’ve attached an image to help understand it.
If it’s a FWD and an automatic and it’s in Park, the tranny output shaft will be locked with a “parking pawl”, but the differential portion of the transaxle will still operate as per the attached diagram and the opposing wheel will spin the opposite way. 
You do, however, have to use a bit of imagination with the diagram and visualize the parts moving and not moving. For example, one axle turning and the other not.
The car is a FWD 2007 Corolla. I just figured that the transmission would lock the wheels @ “Park” and the ignition turned off, of course.
Just curious, otherwise everything is working fine.
It does lock the wheels in park when both wheels are on the ground but the wheels are free to tune as long as they are turning in opposite directions.
This isn’t about your current thread but did you replace the worn tires and now have them inflated correctly that you wrote about in July.
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Your car has a trans-axle, which is sort of a combined transmission and differential in one. P locks the transmission, but not the differential. If the wheels spin independent of the other in this mode – one spins freely while other doesn’t spin at all – that’s an indication of a problem w/ the transmission selector is in P. But if one spins one way and the other spins the other way, that’s normal operation for a differential.
Concerning the tires I wrote about in July:
YES!
I replaced the defective and worn tires with a brand net set of Kumho SENSE tires 195/65R15
They’re great tires, the ride has been vastly improved. Should’ve done it much sooner.
July? Heck, I can’t even remember what I did last week! 
I envy you. I can’t remember why I got up and walked to the next room!
LOL, yeah, that happens to me often.