A Priority Access Period is a special period that Verisign is having for each of their new international language top-level domain (TLD) launches. Verisign is the central registry for .COM, .NET, & .CC, and, now, the new international language versions of .COM and .NET. As they launch these new international language versions of .COM and .NET, they are having what is called a "Priority Access Period" for each domain. During this period, domain owners have the opportunity to register their same domain name on the international language version of their TLD.
For example, if you own yourname.com, you can register yourname.닷컴 during .닷컴's Priority Access Period and no one else can register that same domain name on .닷컴 during this time. To take advantage of Priority Access, you will need to first log in to the Dynadot account that has the exact match domain name you want to register in it. This domain name must have been registered before Priority Access began and it must no longer be eligible for grace deletion. Then, you can search for the matching domain name on the TLD's page, so for the above example, you would need to visit the .닷컴 page (link is below).
Verisign has launched the following new TLDs so far:
.コム - Japanese Katakana version of .COM
Priority Access Period: 3/15/16 00:00 UTC - 5/16/16 00:00 UTC
Landrush Period: 5/16/16 00:00 UTC - 6/13/16 00:00 UTC
General Availability: 6/13/16 00:00 UTC
.닷컴 - Korean version of .COM & .닷넷 - Korean version of .NET
Priority Access Period: 6/20/16 00:00 UTC - 8/16/16 00:00 UTC
Landrush Period: 8/16/16 00:00 UTC - 8/30/16 00:00 UTC
General Availability: 8/30/16 00:00 UTC
Priority Access Period does not have an additional fee. The current price is $12.99 (though this is subject to change per Verisign). Landrush, however, does have an additional fee. Verisign will be launching several more international language TLDs and this file will be updated as we receive more info.