From a forum answer, here are a few bullet points about synonyms in Lightroom:

• You can use them to save on data entry (eg using the common and Latin names of species)
• You can see them by double clicking a keyword in the Keyword List
• See them by switching the Keywording panel to “Will Export” (the Keyword tags drop down box)
• When you export a file, any synonyms are also written into the export file.
• Also, you can search for synonyms in smart collections.