A "rowid table" is any table in an SQLite schema that
The PRIMARY KEY of a rowid table (if there is one) is usually not the true primary key for the table, in the sense that it is not the unique key used by the underlying B-tree storage engine. The exception to this rule is when the rowid table declares an INTEGER PRIMARY KEY. In the exception, the INTEGER PRIMARY KEY becomes an alias for the rowid.
The PRIMARY KEY constraint for a rowid table (as long as it is not the true primary key or INTEGER PRIMARY KEY) is really the same thing as a UNIQUE constraint. Because it is not a true primary key, columns of the PRIMARY KEY are allowed to be NULL, in violation of all SQL standards.
The rowid of a rowid table can be accessed (or changed) by reading or writing to any of the "rowid" or "oid" or "_rowid_" columns. Except, if there is a declared columns in the table that use those special names, then those names refer to the declared columns, not to the underlying rowid.
Access to records via rowid is highly optimized and very fast.
If the rowid is not aliased by INTEGER PRIMARY KEY then it is not persistent and might change. In particular the VACUUM command will change rowids for tables that do not declare an INTEGER PRIMARY KEY. Therefore, applications should not normally access the rowid directly, but instead use an INTEGER PRIMARY KEY.
All of the complications above (and others not mentioned here) arise from the need to preserve backwards compatibility to the tens of billions of SQLite database files in circulation. In a perfect world, there would be no such thing as a "rowid" and all tables would following the standard semantics implemented as WITHOUT ROWID tables, only without the extra "WITHOUT ROWID" keywords. Unfortunately, life is messy. The designer of SQLite offers his sincere apology for the current mess.
SQLite is in the Public Domain.