This would restrict states from imposing certain regulations on a specific living property in the U.S. Constitution. This amendment would give the right to Human property within any state, either free or slave, to the owner either during transportation, temporary visitation or by escape to any state to the recognized rightful owner of another state. Such human property will not be taken away or deprived from or restricted from use by the owner of said property by Federal or by U.S. Territorial law.

This was later basically placed into the body of the Confederate Constitution

This phrase...

"shall stand on the same footing in all constitutional and federal relations as any other species of property so recognized;"

In general relates to this 1841 debate...

The Governments have no power to discriminate, and fix upon one description or species of property greater tax than that fixed by law upon every other description or species of property of equal value, subjected to taxation.

Every individual may lawfully acquire and possess any species or description of property if he does not thereby destroy or deprive some other person of his property. or some enjoyment thereof, in which he is protected by law.

But property, when acquired and possessed, must be so kept and disposed of as not to injure any paramount legal right of another, or affect injuriously the public morals, or public good, so far as they are protected by law.

Below is an explanation of the tax meaning...

"Legislatures cannot, by first prohibiting the use of any article or the exercise of any calling, and then allowing it upon payment of a certain sum into the Treasury, create a privilege. If this could be done, there would no longer be any meaning or effect in the provision that no one species of property should be taxed higher than another species of property of equal value. If this could be done, the Legislature could tax every bureau a hundred dollars, or every table, or chair, or sofa, or book-case, to the same amount‘, merely by prohibiting the use or possession of each article except upon payment of such sum, and so making it a privilege to have, use, or possess it. They might pass sumptuary laws, and tax shoes, boots, hats, coats, cloaks, and every article of dress, comfort, luxury or necessity, by pursuing the same course, and making it a privilege to have, wear, or possess it.

There are certain rights which belong to us as freemen; we do not derive all our rights from Legislative grant; we have some which belong to us by nature, and as citizens of a free country; such are the rights of holding any species of property we choose, of wearing whatever garments we choose, and of possessing and holding any article of comfort or luxury which we please. As all then belong to us originally, they cannot be converted into privileges by any process of Legislative alchemy. No such magical transmutation can be effected. If it could, nothing would be easier than by the enactment of sumptuary laws and acts creating privileges to transform us at one sweep from free citizens of a republic to the mere serfs of the soil.

The right to keep and use a billiard table is one of these common rights. It is an article of furniture which every citizen had the right to own and possess before we framed the Constitution, and the Legislature cannot confer upon us the privilege of keeping what we already have the right to keep and use. Privileges are not so created; if they are, every thing can be transmuted into a privilege, and by undergoing this process, an article of property worth a hundred dollars may to-day be taxed one dollar and to-morrow a thousand, while another article of the same, may still remain subject to the original tax of one dollar."