Sindarin for 'holy song' or maybe 'sea song'
The aerlinn are Elven songs or hymns addressed to Elbereth, or more probably to all of the Valar.
The exact meaning of the word is ambiguous: no word for 'holy' has been attested in Sindarin but it is believed that the equivalent of the Quenya word aira would be aer. On the other hand aer means 'sea'. In that case theses songs express their longing for Valinor beyond the Sea.