Hi, I don't quite understand it myself but I looked it up in the dictionary for you and as I understand it and as a mature student you probably know that it all relates to Freud - Psychodynamic is when a person's personality, that is their behaviour or attitude shows not only their conscious mind but there is an underlying unconscious factor at play which they are not aware of. So there's a dynamic relation between the conscious and the unconscious. E.g You're angry all the time but don't realise that the anger may be due to some childhood trauma or repressed desire?
Psycoanalytic - Is basically the structure of theories which look at that relation between the conscious and the unconscious.
I can tell you what Psyco means? That just simply means 'Nutcase!'
Hope this explanation is helpful although it maybe a bit basic for you?