Stripped of legalese, it means together or separately.
If three friends, A and B (two persons with few assets), and C, who is wealthy, borrow $10,000 from Z and agree to be joint and severally liable for the full amount, and they then default on the loan, Z can sue and collect the full amount against all three or against C only, not having to worry about collecting from A and B (that would then be C's problem in private actions for contribution from A and B).