Generalise is the British spelling of generalize. The word means to take a few cases and make a wider claim — to say ‘this is how it usually is’. Scientists generalise from results; everyday people generalise from one bad meal to ‘that whole street is awful’. Used kindly, it is how we learn patterns. Used loosely, it turns into a unfair jump: one person, then ‘they all…’. Teachers and newspapers in Britain often write -ise (generalise, organise). American books write -ize (generalize). Though actually, some British publishers, including Oxford, prefer -ize even in Britain; most British school English still teaches -ise. The meaning does not change with the spelling. You can also generalise a rule so it covers more cases, or speak in a generalising way when you do not want to be exact.