The conjugate base of a compound is what this compound will be after donating a H⁺.
The comopund in question is H₂BO₃⁻. After it loses 1 H⁺, it will have one less H atom and its charge decrease by one. Its charge is only with a "-" sign, which means its chargeis 1-. After decreasing by one, the charge becomes 2-.
So, the conjugate base will be HBO₃²⁻