I.e., my feelings for you are those of friendship, not of romance. 'Tuus amicus' is in apposition with the subject nominative implicit in 'amo' (i.e., 'ego', 'I').



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Note added at 30 mins (2006-03-21 00:39:46 GMT)
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The order of the words is emphatic, as the order of words in Latin sentences routinely is--in this case because 'tuus amicus' begins the sentence, but also because 'tuus' precedes 'amicus'. A more accurate, if less literal, rendering would therefore be, "It is as YOUR [not as somone else's] friend that I love you".

I should also note that the verb 'amare' is sometimes better translated by 'to like', since it does not always have a romantic or sexual connotation, but is freely used to express affection of all varieties.