I think honoring the tradition means knowing as much about the song as possible. When was it written and by whom, if known. What is it about and what was the original historical context. What do the words mean. What tune or tunes has it been sung to. Who has sung it in the past and what interpretations have they given to it.
Knowing this, you can then give it your own interpretation. You might even change the words or the tune or style - you don't need to copy exactly the way you've heard someone else sing or play it. But you should honor the original meaning and history of the song.
Too often I've heard newer singers take a song and completely change it so that the playing of the tune (tempo, style, etc.) has no relation to the words that are sung or the message that the song is trying to convey - too fast, or too slow, or a strange mixture of styles. Often times the words are not even understood - as if the words are not important.
Sometimes it takes a long time of singing the song until you finally realize what it is about, what the words really mean, or how the tune fits with the words. It may be a slow evolution or a sudden realization. But knowing as much about the song as possible helps.
The you should always give credit and attribution to those who have contributed to the the song and its history.