It means that the same entity that "meant" for Bilbo to find the Ring, also "meant" for Frodo to have it, and to go on the Quest of Mt. Doom to destroy it. That entity presumably is indeed Eru Iluvatar, and being the All-Seeing and All-Knowing, he knew that Frodo would be the only one who would even remotely succeed in destroying the Ring. Then again, even Frodo failed, but another Ringbearer might have failed earlier in the journey. It was pure luck that made Frodo fail right in the Sammath Naur, otherwise, Gollum wouldn't have been able to bite off Frodo's finger and fall into the lava.
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But Melkor also was there, and he came to the house of Fëanor, and there he slew Finwë King of the Noldor before his doors, and spilled the first blood in the Blessed Realm; for Finwë alone had not fled from the horror of the Dark.
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