Portobello or portabella mushrooms are really just cremini mushrooms that have grown large, and creminis are really just one form of the humble button mushroom. Once upon a time these overgrown shrooms were thrown out, until sometime in the 1980s someone got the brilliant idea of marketing them under a faux Italian name as a delicacy. And so the portobello was born.
Portobellos have flat caps which can be 6 inches or more in diameter. As they grow from little creminis the caps open and spread, exposing the gills, through which some of the moisture evaporates, creating a concentrated flavour and dense - some would say meaty - texture. Portobellos have very woody stems which for that reason are not usually eaten; only the caps are consumed. They can be sliced or chopped like any mushroom, or left whole and grilled.
Like any mushroom, portobellos should be washed under a gentle stream of water before being used. (I don't subscribe to the school of thought that mushrooms in water get water-logged.) When they are fried, the gills cause the mushroom flesh to become quite black, so you may want to slice off the gills with a sharp knife first. Store them in a paper bag if you have one; they will go soft and stinky stored in a plastic bag unless it's really airtight.