Is DB-25 port Serial or Parallel?
A DB-25 connector could be serial port or parallel port or something else.
A DB-25 connector is a generic connector.
It is not exclusively used by just one interface (like HDMI or USB connectors are).
On a modern PC, a DB-25 (especially a female connector) is typically associated with a parallel (aka LPT) port.
On older computer and telecommunication equipment, a DB-25 connector is typically a RS-232 serial port.
Prior to the mid-1980s, RS-232 ports typically used DB-25 connectors.
Printers used RS-232 interfaces and/or custom interfaces.
One of those interfaces, a parallel interface using a 36-pin connector developed by Centronics, became an industrial and then an IEEE standard.
When IBM introduced its PC, it substituted the large Centronics connector with a slimmer female DB-25 for the LPT port. The female DB-25 connector was typically used for DCE RS-232 ports (e.g. a phone modem), and this was a new application for that connector. The RS-232 port(s) on the IBM PC used male DB-25 connector(s).
When IBM introduced its second-generation PC/AT, in 1984, IIRC it substituted the large male DB-25 connectors for RS-232 ports with "DB-9" (actually a DE9) connectors that today's users associate with "serial" ports. The parallel LPT port continued to use the female DB-25 connector.