I do not wish to post any longer but as a clarification for others, I want to explain the meaning of this phrase. Believe me, it is most esoteric.
It means 'Come to Me Alone for Refuge'.
I would like to explain the terms in the reverse order because it is easier that way.
Vraja: It means 'Come'. But 'Come' for what? See the next term.
Sharanam: It means 'Refuge'. 'Refuge' means something like 'shelter' or 'a rest place' or 'a place of relaxation' or 'be happy in' or 'be at peace in'.
Yekam: It means 'Only' or 'Alone'. It means leave groups like country, race, caste, language, club, relatives, friend-circle, religious affiliations, neighborhood, humans etc. In essence, it means leave every group that is limiting.
Maam: It means 'Me'. But what is 'Me'? It's a bit tricky to understand but with patience it can be understood. Even if not understood exactly, some knowledge of it is enough to live a practically happy life. So is it an individual called Krishna who is supposed to have lived some thousands of years back? Or is it one's own individuality? Or is it some self-acclaimed God-man. No! The answer is surprisingly simple and even a lay-man has a good grasp of it. But since we are swept away by Maya i.e. illusion, we lost this knowledge that we actually had when young. The key to understanding 'Me' lies in understanding what is 'me'. 'me' refers to an individual and so 'Me' cannot an individual. Since 'Me' is an emphasis of 'me' and there are many 'me'-s in the universe, it means that 'Me' is the collection of or what is common in many 'me'-s. If Sherlock Holmes had never got to read the Bhagavad Gita and came across only this phrase scribbled on a piece of paper, he will probably say Elementary, Mr.Watson.