Good question Abe.
Here goes! I found some great sources of info for you, too.
In a closed primary, only voters registered for the party which is holding the primary may vote. For instance: if the Democratic Party is holding a closed primary, then only voters registered as Democrats are permitted to vote in the primary.
In an open primary, any registered voter can vote in any party's primary. Voters choose which primary to vote in (voters must choose ONE); they do not have to be members of that party in order to vote. For instance: a registered Democrat can choose to vote in the Republican primary but NOT BOTH Democratic Primary AND Republican Primary.
Not finished yet...
In a semi-closed primary, unaffiliated voters can choose which party primary to vote in, while voters registered with a party may only vote in that party's primary.
For more information...
Below are several great links to both help explain the process further AND display state-by-state info for you.
Open vs. Closed vs. Semi-Closed:
Congressional Primary Type (by state):
Presidential Primary or Caucus Type (by state):