He is looking at the jackets.
Han tittar på en jackor
the correct translation ?
It's en jacka, jackan in the singular, and jackor, jackorna in the plural, so He is looking at the jackets would be Han tittar på jackorna.
Can we use "Jag ser" as in English "I see" to mean "I understand"?
No, not in a brief form like that. It works for e.g. Jag ser vad du menar ("I see what you mean"), though.