Simple administrator authentication page in PHP
You should not store your password in plaintext, as this means that read access (eg via LFI) automatically leads to more (probably some sort of write access via the admin backend). Use bcrypt for this (this also solves the next point automatically).

Ideally, you should also use some sort of timing safe string comparison.

Ideally, I would move the user credentials into an extra config file, which can be placed outside the web root (in case the connection breaks up while a user edits the file, which may lead to a backup file like login.php~ or similar being created, which may be severed by a webserver).


  I plan on adding things like halting the script for a few seconds depending on how many attempts were made from the current session.


I guess that is one solution, but I would just deny attempts completely for x seconds if y attempts where made from that IP in the last z seconds.

Misc


You are overdoing it a bit with comments, which leads people to ignore your comments. Comments should not rephrase what the code already told us, but add additional information in case the code is unclear (Username =&gt; Password and possibly Expiration time in seconds/Array of authenticated users are the only comments I would actually keep).