table is the name of the table in the database. $database in your example will contain a result set of rows from the database according to the query passed into the mysql_query function. It should probably be named $result instead of $database to give you a clearer understanding of what is happening.

Try to think of a database being like a filing cabinet. The tables in the database are the files in the filing cabinet and store the actual data.

EDIT: To actually connect to the database in php, check out the mysql_connect function. Once connected you run SQL queries using the mysql_query function and interrogate the result with the mysql_fetch_* functions.

Thanks darkagn. I guess a better way to phrase my question would be is it possible to only select one row at a time based on something like the primary key? Something along the lines of:

your question is rather vague, if you're asking how to limit the results by a condition then almostbob asked your question.

If you meant columns by 'rows' then u asked the question yourself by:
$result = mysql_query("SELECT column FROM table");
but If you want efficiency, meaning finding something fast in a database, well, I guess very few people had trouble with this, and I think you don't have to worry about efficiency in this case.