wikipedia helps.

Saudade (singular) or saudades (plural) (pronounced [sɐ.uˈdaðɨ] or [sawˈdaðɨ] in Portuguese,[1] is a Portuguese word that can be translated as "longing, yearning", which describes a deep emotional state of nostalgic longing for something or someone that one was fond of and which is lost. It often carries a fatalist tone and a repressed knowledge that the object of longing might really never return.
Saudade has been described as a "vague and constant desire for something that does not and probably cannot exist ... a turning towards the past or towards the future".[2] A stronger form of saudade may be felt towards people and things whose whereabouts are unknown, such as a lost lover, or a family member who has gone missing. It may also be translated as a deep longing or yearning for something which does not exist or is unattainable.
Saudade was once described as "the love that remains" or "the love that stays" after someone is gone. Saudade is the recollection of feelings, experiences, places or events that once brought excitement, pleasure, well-being, which now triggers the senses and makes one live again. It can be described as an emptiness, like someone ( e.g., one's children, parents, sibling, grandparents, friends, pets) or something (e.g., places, things one used to do in childhood, or other activities performed in the past) should be there in a particular moment is missing, and the individual feels this absence. In Portuguese, 'tenho saudades tuas', translates as 'I have saudades for you' meaning 'I miss you', but carries a much stronger tone. In fact, one can have 'saudades' of someone whom one is with, but have some feeling of loss towards the past or the future.