Gram positive (G+) and Gran negative (G-) relate to results from a test called Gram staining, named after a guy with the last name of Gram..
Gram staining is typically used for diagnostic tests, finding out the species of an "unknown" bacteria.
It involves staining the bacteria with crystal violet. This shows up as a purple colour when looked at under a microscope. The crystal violet actually stains a part of the cell wall known as the peptidoglycan layer (basically made of amino acids and sugars). Only bacteria with a thick peptidoglycan layer retains the crystal violet once it’s been washed with iodine solution. Those that do keep the purple colour are know as G+, they have a thick layer. If the crystal violet gets washed out, then it means the bacteria’s peptidoglycan layer isn’t thick enough to trap the crystal violet molecules and so are referred to as Gram negative. To be able to see these G- bacteria under a microscope, they need to be stained with safranin (gives a red colour).
If cell wall has thick peptidoglycan layer= Gram positive, purple
If cell wall has less peptidoglycan= Gram negative, red-ish