Skyler's Apartment is where Skyler White lives with her son Walter White Jr. and her daughter, Holly White. They moved there after Walter White's criminal activities became widely known and their former home was seized from them by the DEA.
While Walt was in hiding in New Hampshire, he got information about his family from Ed and newspapers brought to him by Ed. At one point Walt asked if his family had found somewhere better to live, Ed said, "no". ("Granite State")
Before going to meet the white supremacist gang at their compound that evening, Walt visits Skyler at her place. He explained himself to her, gave her the coordinates for the grave of Hank Schrader and Steve Gomez so that she could better bargain with the federal attorney. He then spent some time with Holly in the bedroom shared by her and Skyler, and from a little way off watched Walter Jr. come home from school before leaving.("Felina")
It can be assumed that, following Walter White's death, Skyler, Walt Jr and Holly inherited his money through the trust fund established by Elliott and Gretchen, allowing them to move into some place better.