A lot of loricariid catfish get traded before they are identified by scientists. So they don't have names, at least, not scientific names (e.g., Hypostomus plecostomus). To make it easier for collectors, exporters, retailers and hobbyists to talk about one particular catfish, these unidentified catfish are given L-numbers. Think of them as interim names.
Once the catfish is described by scientists and given a proper name, in theory the L-number can be retired. In practise some aquarists find the L-numbers easier to remember than their scientific names, and so stick with the L-numbers.
Simple as that!
Actually, it's a bit more complicated because sometimes a bunch of different L-number catfish turn out to be mere variations of one species. Sometimes one L-number ends up being given to a bunch of genetically distinct (if superficially similar) catfish.