Here is how Wikipedia describes it:
Saudade is a Portuguese word that has no direct translation in English. It describes a deep emotional state of nostalgic or deeply melancholic longing for an absent something or someone that one loves. Moreover, it often carries a repressed knowledge that the object of longing will never return.
Saudade was once described as “the love that remains” 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 or something (e.g., places, things one used to do in childhood, or other activities performed in the past) that should be there in a particular moment is missing, and the individual feels this absence. It brings sad and happy feelings all together, sadness for missing and happiness for having experienced the feeling.
This pretty much captures my state of mind and soul these days. I move through my busy life, having dinner with friends, traveling for work, meetings with clients. But the moment things are quiet, when I have times of transition—I return home from a trip, have a few spare minutes before moving on to another activity, or something funny happens, or I watch a show we used to watch together or discuss on the phone—I am snapped back to the loss.
It is hard to explain the persistent disbelief, when my mind fleetingly thinks, “I should call mom,” or I refer to her in the present tense. It feels a little like a cartoon. You know, the one in which the character has had a cannon blown through his body and there is a big gaping, smoking hole in his chest. Yet he doesn’t realize it until he looks down.