Carbonic acid reacts with water to yield bicarbonate ions and hydronium ions: h2co3+h2o⇌hco3−+h3o+ identify the conjugate acid-base pairs as: acid conjugate base base conjugate acid !

For the equilibrium that you have written... 
H2CO3  +  H2O <==>      HCO3-    +              H3O+ 
acid            base       conjugate base            conjugate acid

We know that carbon dioxide reacts with water to form "carbonic acid." However what we really call as carbonic acid is not the weak acid H2CO3; H2CO3 does not even exist in aqueous solution. What really we call as carbonic acid is simply CO2 dissolved in water which is in equilibrium with small amounts of H+ and HCO3-. HCO3^- is the intermediate substance between CO2 and CO3^2-. By adding OH- to HCO3^- we produce CO3^2-. Adding H+ to HCO3 produces CO2. 
CO2(aq) + H2O(l) <==> H+ + HCO3^- carbonic acid midrange pH values 
HCO3^- + OH- <==> CO3^2- + H2O(l) formation of carbonate ion basic 
HCO3^- + H+ <==> CO2(g) + H2O(l) formation of carbon dioxide .. acidic

Acid: H2CO3

Conjugate Base: HCO3-  

Base: H2O

Conjugate Acid: H3O+