They mean nothing, absolutely nothing. The Russians are no fools and they know this very well. It's all for show, for the media.
That said, from a scientific standpoint, I have to say that the Russians are far more advanced that the other four Arctic states in terms of their knowledge of the geology of the Arctic polar basin. It began with the Papanine expedition in 1937 and, if I'm not mistaken, they have now reached station 45. They know the geology of the Arctic polar basin.
In 1974, the Russians published a geological map showing the location of the Lomonosov Ridge. The Americans maintain that this ridge contains approximately 25% of the world's oil reserves. The ridge is a disputed area. Russia is claiming ownership of this shelf, a position disputed by Denmark and Canada.
Generally speaking, from a scientific and legal standpoint, the level of cooperation is fairly good. Not long ago, on Mary 28, 2008 to be precise, the five coastal Arctic States made a declaration in Greenland. These five States get along very well. Despite the Russian flag-planting spectacle, the States do get along.
The Law of the Sea provides for important rights and obligations concerning the delineation of the outer limits of the continental shelf. The protection of the marine environment, which of course is immensely important there, includes ice-covered areas, freedom of navigation, marine scientific research, and other uses of the sea. This is the important part. We remain committed to this legal framework and the orderly settlement of any possible overlapping claims.
It's important to emphasize that although the United States are not yet a signatory to the convention, they have expressed their support for the declaration of the leaders of the five coastal Arctic states.
So then, to answer your question, the gesture is meaningless.