Black stuff in garden, what is it?

We don't get a lot of them here, as it's apparently fairly common for heavy clay to have low levels of worm life.
If you give your lawn a bit of food through the growing season, and leave it a bit longer, you'll notice them less @nav. When it's dry, you just brush or rake them off, as others have mentioned.
If you're needing to cross the lawn regularly, it might be better to put a path in to save being on the grass. The grass doesn't look in the best of health, so maybe there's a bit of compaction etc needing attention.
Are you in the UK though? I don't think many folk are trundling around on their grass barefoot at this time of year!