In addition to being dropped, a single fragment can be crafted by combining one of each of the other three types. For example, if a player were missing a Solar Fragment but had a surplus of all the other types, they could combine a Vortex Fragment, Nebula Fragment, and Stardust Fragment into one Solar Fragment. This is done at the Ancient Manipulator.
It is likely that the ability to craft a single type of fragment (Solar, for example) from the other three fragment types (Nebula, Vortex, and Stardust, in this case) was implemented due to the arduous process required to collect each fragment. For example, being a single Solar Fragment away from crafting the full set of armor would otherwise mean that the player had to again fight the Lunatic Cultist and the Solar Pillar. Furthermore, it allows players to craft items that require all four types of fragments, such as the Super Healing Potion, prior to taking on the Moon Lord.
The fragments each correspond to a weapon class. Solar Fragments are used for melee weapon users, Nebula Fragments for magic users, Vortex Fragments for rangers, and Stardust Fragments for summoners.
Lunar Fragments are not affected by gravity, similar to souls.