Looks like mildew.
What is the tarp made from ?
Basically bleach will kill the mould's spores, and help remove the stains, but it needs to be used with care. Too much can weaken natural fibres, and remove colour from the fabric. It doesn't need to be strong to kill the mould though. It just needs to be thoroughly done and aired dry.
Vinegar can work too, just make sure you really, really rinse it well afterwards or it can attract insects and mice.
Mildew is basically a problem of storage. Above 67% humidity and the mould will grow. Some fibres, like cotton, just soak up moisture.