There are 3 interpretations to the word "Sharanam", all of them looking at the same reality from a different angle.
"Sharanam" as referring to falling at the feet of the Lord...
The Sri Vaishnavaites like this interpretation very much. It's because they feel they are a privileged lot and want to be rid of class distinctions.
"Sharanam" as referring to Surrender of the ego to the Lord...
This is a much finer interpretation than the previous one. Vibishana surrendered to Rama knowing that Rama will not let down those wanting his friendship. Even when everyone advised against taking VibishanA as it may be a military strategy of RAvanA, Rama said that he cannot deny protection to anyone seeking Him, even if it meant he may be a traitor.
"Sharanam" as taking Refuge in the Lord...
