It means "affectionate" in a general manner.
In Spanish a person may be "entrañable" and something is "entrañable" when related to a person we have affection for.
But right now, I can't figure out a word for it in English, I hope I explained it well enough.
Wow - I have no idea how to translate that - maybe "important" (implying that it's important to the birthday person, and the writer knows that, so s/he's expressing his/her affection)?
un dÃa "entrañable" es un dÃa "especial" con un matiz de nostalgia, como cuando te reunes con la familia en ocasiones especiales como en Navidad, esas reuniones son "entrañables"
Sorry bodhi, I don't think "entrañable" implies nostalgia at all, it may contain tenderness, intimacy, closeness, but not a bit of longing for the past.