It means the soldier in question was captured by Federal forces and immediately paroled that day upon, either, taking the oath of allegiance to the United States, or swearing, for example:

"That I will not take up arms against the United States, nor serve in any military, police, or constabulary force in any Fort, Garrison or field work, held by the Confederate States of America against the United States of America, nor as guard of prisons, depots or stores, nor discharge any duties usually performed by Officers or soldiers, against the United States of American, until duly exchanged by the proper authorities."

Vicksburg, Mississippi parole certificate, ca July 1863.

George Martin