Portamento is a musical term, meaning, basically, sliding between two notes on the sheet music instead of crisply hitting the first, then the next. But more generally it means all the little stuff singers do instead of singing mechanically.
Portamento is musical seasoning. You've have soup that was too salty, right? And soup that lacked salt. Neither is fun to eat. Ditto portamento. Bad singers use portamento like bad cooks use seasoning: to mask the fact that the basic ingredients aren't very good.
In opera, for example, singers who aren't sure of just exactly where that high note is will sliiiiiide up to it, hoping to come across it--though like as not they still sing the note a bit flat anyway. I've heard opera singers and country music singers and pop singers all abuse portamento this way. The better your pitch sense is the more annoying this becomes.
But imagine hearing someone with no musical imagination sing something without any note-bending, without any accelerations or hesitations, nary a gospel lick, nor blues lick either (very closely related, those)--and you're back to that bowl of soup that tastes like hospital food.
I've heard singers with un-beautiful voices make their bones as song stylists--which is perfectly acceptable. I've also heard singers with beautiful voices (like Barbra Steisand) overuse portamento--as if they didn't trust their own basic materials.
Listen to Jackie Evancho sing anything for an example of using portamento just right, within the scope of her genre ("classical crossover"); to Bonnie Raitt for bluesy pop; to Mahalia Jackson for straight-from-the heart gospel licks; to Dulce Pontes, La Albita and Elis Regina for Latin music... Those singers will teach you most of what you need to know about portamento.