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and/or is a useful way of writing notes. It means "and or or" (and the more nit-picking variety of spellcheckers won't pester you by pointing out to you that you have duplicated a word). Nevertheless, it is not acceptable in formal academic writing: you should avoid abbreviations. In your assignments, write the full three words, and or or. (Ignore what the spellchecker will tell you.)

In many contexts, the three words are unnecessary. The word 'or' is not usually the 'exclusive or' (symbolised in computer logic by XOR, which is different from OR). It would be foolish to fuss about whether the question "Milk or sugar?" is logically accurate; we all know that this is not an exclusive 'or': you can have both. In academic English, however, 'we all know' is not enough. The writer's job is to say what she (or he) means. And sometimes, the construction and or or will be necessary. When it isn't, don't use it.