It means "no, not really." Example: Q.Do you like eating liver or tripe? A. No, not particularly.

"Not particularly" basically means "not very much." If someone asks you if you like something, and you don't like it very much, but you also don't completely hate it, you might say "Not particularly." Likewise, you might say "I don't feel particularly well today" if you aren't horribly ill, but you feel a little sick or upset.

We use this when we don't really like something or don"t want to do something

Not particularly is a weak form for saying I don't like something or don't want to do something. 'Would you like to go to the cinema tonight?' 'Not particularly'.