While any large database may have errors that can lead to multiple entries (sensu har-wradim's answer), I think most of the multiple entries detail the taxonomic history associated with that species. Your link to the sponge Haliclona digitata provides a clear example. First, dismiss the H. digitata (Schmidt, 1862) entry. As clearly stated, it is a synonym for a different species of sponge, Tedania anhelans.
The remaining entries are all links to various homonyms of H. digitata. Skimming through the World Porifera Database entries (via the "Online resource" links), provides the necessary information. Lendenfeld's use of Chalinorhaphis is the original description. It is the senior homonym, meaning the specific epithet (digitata) has precedence over junior names. The junior names include Adocia digitata (Baer) and Gellius digitatus (Koltun). It was probably Tanita & Hoshino that transfered digitata to the genus Haliclona but I cannot verify this without seeing the article.
The taxonomic history can also be tracked for Ichneumon varius, but the linked databases don't hvae as much detail as the Porifera database for H. digitata. Still, it suggests that the description by Pontoppidan in 1763 is the senior homonym, and the subsequent uses by Cuvier, Gmelin and Muller are junior homonyms.
This is also what I think har-wradim is alluding to for Pimpinella dioica. Unfortunately, the Umbellifer database seems to have little detail in this regard.
The Catalogue of Life provides a convenient mechanims to begin a thorough search for the taxonomic history of a species.