Vongsense was a power which enabled a being to sense Yuuzhan Vong telepathically. This ability was discovered by Anakin Solo after he attuned a lambent crystal to him and then repaired his lightsaber using it.
This ability was fairly rare, although it was also possessed by Tahiri Veila, Finn Galfridian and by Anakin's brother Jacen. This was because forming it sometimes required a physical or mental connection of sorts to Yuuzhan Vong biotechnology. In Anakin's case, this was the lambent crystal; in Tahiri's, the vivisection she had suffered as the captive of Mezhan Kwaad; and in Jacen's, the similar ordeal he had undergone at the hands of Vergere.
Vongsense proved to be an asset to the Jedi in winning the Yuuzhan Vong War.
Some Jedi practitioners would have to temporarily abandon their connection with the Force in order to use Vongsense. Karness Muur, Allana Solo, and the One Sith did not.
Despite most other cases of Vongsense being a result of a connection to Yuuzhan Vong biotechnology, Finn Galfridian's ability to use Vongsense was not explained. Karness Muur (while possessing Celeste Morne), Allana Solo, and most One Sith also did not have such a connection.