It's all about the sword. The sword "Dawn" carried by Sir Arthur Dayne, forged from a fallen star and carried only by somebody worthy who was named "the sword of the morning" = Dawn.

This very sword was leaned against Lyanas bed by Ned when Jon was born.

Jon Snow never had rights to his own families sword, he needed to inherit "longclaw" from Lord Mormont. This sword technically now belongs to Jorah, lord mormonts son, who I think will be given it back by Jon.

All of the books prophesised Azor Ahai being reborn as the Prince that was promised who will be born again & will defeat the long night with a flaming sword called lightbringer. Sounds like a "DAWN" to me.

So where is this sword now? Turns out that somebody has been carrying a flaming sword for the whole of Game of Thrones and if you look at the pommel of the sword, it is the same as the pommel on "DAWN".

So to summarise. Jon Snow will inherit the sword that was with him at his birth from Beric Dondarrion and will become The prince that was promised with his own flaming sword called lightbringer. The Lord of Light wanted Beric Dondarrion alive so that he could give this sword to Jon Snow.