Explain Jefferson's quote, "I believe that states can best govern our home concerns, and the general government our foreign ones."

Thomas Jefferson was an antifederalist.  This means that
he was generally in favor of the states having more power than the federal government. 
That is what he is saying in this quote.

Jefferson is
saying that the state governments should have the power over everything that is domestic
policy -- things that do not involve foreign governments.  For example, Jefferson would
have thought that states should control taxes and things like that.  He thought that
this would keep the national government from imposing bad policies on the states the way
that England had imposed bad policies on the colonies.

But
he is also saying that the national (what he calls the "general") government needs to
take care of foreign policy.  The states should not be able to form separate alliances
with other countries, for example.

So he is saying that the
state governments should handle domestic policy and the national government should
handle foreign policy.