Meaning

It is not precise, but a local concern would be some issue in my neighborhood or city. In the US, we have world / international news, national news, state news and local news, and concerns at each level.

So can an issue that is in a national level can also fit into a local level. Because I am writing an essay about an issue of local concern. I know fixing a road would be obvious to be a local concern, but how about immigration, people with different cultural backgrounds? It's more a national level thing, but can I talk about it in a local level, and then somehow bring it up to a national level?

It is more of a strictly local level if local laws can be passed to alleviate the problem.
In the case of immigration, it may be a local concern especially on the border states, but it cannot be addressed locally, only nationally. In that case, the locally elected officials and representatives will propose and try to get laws passed at the national level.

Oh, so can I say immigration is a local concern, and the solution is to address it to national level? because the topic also asks me how to address it?

Immigration in the US affects some communities more strongly than others, so although it's a national issue, there may be aspects that are of greater local concern. For example, the states along the Mexican border have different types of concerns about immigration than communities that rely on migrant farmers (who are often immigrants).