No, it means the service provider in her area does not cover the phone. So if you were to travel to your mother's, you'd probably get bad service.
Madge, the "Check to see if it works in your area before you buy" box is mainly for Walmart/Straight Talk marketing purposes and is NOT a true indication of where the phone will "work."
Since this particular Straight Talk phone uses the Verizon "native" network, you will be able to use it anywhere in the U.S. where Verizon Wireless has "native" coverage (native coverage = towers that Verizon owns so, in other words, no roaming privileges on other networks).
Verizon is considered by most to have the largest coverage footprint in the U.S., so chances are you will have coverage in most areas as you travel in the country (except Alaska where there is no native Verizon coverage).
It will NOT matter where you mother lives, you will be able to call her as long as YOU are within the Verizon coverage area with this phone. Your mother does NOT have to have Straight Talk service or Verizon service. She can have a cell phone or a land line and you will still be able to call her as long as YOU are in a Verizon coverage area with this phone.
If you are curious as to where you will have coverage, you can view the Verizon street-level coverage map ...put in your address, your mother's address (should you want to use your phone when you are visiting her) or any other address where you think you'll want to use this phone (copy-and-paste):
Check the "Prepaid" button after entering an address or ZIP code and then hit the "Refresh Map" button. The purple-shaded area will essentially show the native coverage.
BTW, if you are interested in ordering this phone, I see that Walmart is offering it with a $25 gift certificate so when you're ready to buy, order if from the following page as it will essentially give you the phone for $74.88 (copy-and-paste):