The interpretation I’ve heard from the imams I know are that it has to do with equity in the marital relationship.
Men are required by sharia law to provide for the basic household needs of their family, in return, their wife has an obligation to honor them and treat them with respect. Because of the way marriages are contracted, women have control of the bridal mahr and their dowry, so in practice women usually have a lot more financial power over the household than men do, even though men are obliged to support their family at a basic level. So, a man may contribute his earnings to his family, but still have little say in how they’re spent because the wife is accorded most of the financial management of the household under sharia law. To even this out, sharia gives men certain entitlements in their families - namely that they have a right to sexual relations (within reason, men are not allowed to rape their wives and are required by the commandment to look after their well-being so they’re not allowed to compromise their wife’s health either mental or physical) and to peace within the home (so, if a man makes a reasonable request, the woman is required to honor it, and women are responsible for seeing that the men in their family are just as well-cared for as anyone else in the home).
So, if a woman is being obstinate, her husband should first gently try to correct the behavior. If that doesn’t work, then he should cease sharing her bed for awhile. If that doesn’t work, then he has the right to more serious measures depending on the specific school of jurisprudence and time period. I looked up a reference about this earlier, and at least one medieval jurist said that a man who ever hit his wife with anything larger than a toothpick was committing a grievous sin and the woman would have grounds for a judicial divorce. Another indicated that physical violence according to this rule was to be limited only to cases of infidelity.