This comes up constantly, usually because a decree was never actually obtained, or because an appeal period had not expired, or because a foreign decree turned out not to be recognised in India.
The civil consequence
Under Section 5(i) read with Section 11 of the Hindu Marriage Act, 1955, neither party may have a living spouse at the time of the marriage. A marriage in breach of that is void, not merely voidable. It is a nullity from the beginning, and either party can obtain a declaration to that effect.
The criminal consequence
Bigamy is an offence under Section 82 of the Bharatiya Nyaya Sanhita, 2023, which carries forward Section 494 IPC, punishable with imprisonment up to seven years and fine. Where the second marriage was contracted by concealing the first, the punishment is higher, up to ten years. It is a non-cognizable offence and ordinarily requires a complaint by the aggrieved spouse.
A decree of divorce does not take effect for remarriage purposes until the time for appeal has expired, or the appeal has been disposed of. Remarrying the week the decree is pronounced is a real and recurring mistake. Confirm the position with your lawyer before fixing a date.
Where the parties are governed by different personal law
Muslim personal law permits a Muslim man to have more than one wife, subject to its own conditions. That is a genuine difference, but the Supreme Court has held that a Hindu man cannot escape the bigamy provisions by converting to Islam in order to contract a second marriage; the first marriage continues to be governed by the law under which it was solemnised.
The position of the second spouse and the children
The second spouse, if the marriage is void, does not have the status of a legally wedded spouse and the succession consequences are severe. However, Section 16 of the Hindu Marriage Act protects the children of a void or voidable marriage: they are legitimate and inherit from their parents, though their rights in coparcenary property are more limited.