I am looking at getting a new jacket, but find the warmth descriptions vague. If a jacket is listed as "warm," in the product description, what does that mean?
So, this is in agreement with everyone else, but just stated in a different way. A jacket cannot, and will not "make" you warm. A jacket's only function is to retain the heat your own body generates, and shield it from the forces of the environment that would accelerate the loss of your body's heat, like wind, rain and snow.
And, warmth itself is a variable as everyone's individual tolerance for cold varies widely. And, your body tends to acclimate to the prevailing conditions. I live in the Mid-Atlantic, and 60F in September is chilly, and I'll put on a jacket, while 60F in March is balmy, and I'm likely to go out in just a t-shirt and shorts. For someone living in Alaska that scenario may play out at 40F. Level of activity was already covered well (pun intended) by @Diesseldorf , so I won't elaborate, but that is a critical component for calculating the amount of warmth provided.
Like others have said, layers are the key, and, if you have the means, and live in, or visit an area with widely varying tempersature ranges, get multiple different jackets to suit each condition, or to layer together. Just as an example: A fleece or sweater for 50-60F. A puffy vest or hybrid for 40-50F. A thicker puffy for 30-40F. A shell for wind & rain. Layer them together as conditions warrant.
And don't forget the importance of a hat or hood, as well as your socks and the pants you wear. The same jacket will keep you warmer under the same conditions if you are wearing a hat. And if your feet and legs are cold, no jacket will really make you feel comfortable.
Unfortunately, there is no single jacket that can meet everyone's own version of warmth.