Only; sole; unique. Refers to something that is one-of-a-kind or the only one and can be used as an adverb or noun modifier.
彼はチームで唯一の医師だ。
He is the only doctor on the team.
この大学が私の第一志望で、ここが唯一合格した学校だ。
This university was my first choice, and it's the only school I was accepted to.
唯一無二の存在という表現は、その物や人が他に代えがたいことを強調する。
The expression 'unique and unparalleled' emphasizes that something or someone cannot be replaced.