Being grounded means that we are trying to make our scene and our characters look authentic, realistic, and believable. We do this by committing to the environment and the reality of what is happing and who we are and what our emotion is.
When thinking about being grounded, we can have grounded characters, grounded emotions, grounded situations, grounded realities, etc. Whatever the scene is, being grounded is in essence being believable.
Gandalf in Lord of the Rings is a magical wizard, but the character is grounded in reality and the things Gandalf says and does are believable based on who Gandalf is, where Gandalf is, and what/why Gandalf is doing (it).  The grounded reality of Gandalf is different then the reality of Bugs Bunny, or the reality of a character that is playing a chicken, or really the reality of any other character an improviser may play. Having belief and commitment within your characters reality can keep us grounded.
Grounded is also the reality of where we are. The reality of outer space is different than the reality of the kitchen breakfast table. If we are in the old west grounded might be opening western doors, spitting in a spittoon, having a cowboy hat, etc. But if we are in this western scene and we go and ask for a Monster Energy Drink that is not grounded in our reality. Yes it might be funny, yes it might be playable, yes it is an unusual thing and might spin into a game, but it is not grounded. Grounded is treating the situation as if it is real. If we are in the old west and I am a cowboy I want to play the reality of a cowboy in the old west, maybe I’m a cowboy who is mad at my partner because they keep trading our goods for chickens, which might be unusual, but I’m still a cowboy, will respond as a cowboy, and play the grounded reality of a cowboy who is mad at my partner for trading our goods for chickens. If I start talking about radio active toxic chickens out of no where this is not grounded, if my partner trades 10 more items for chickens and I change my character to now be happy about the chickens my characters emotion isn’t grounded. If our grounded base reality is fear, grounded is keeping in line with our fear, we might build an arc and make a fearless decision later in the scene, but if we are afraid, we need to play the reality of our fear.