A dry tongue and a growling belly will motivate most folks to work. There is a reward for work, and that reward allows the worker to satisfy hunger and thirst with groceries.

That's easy to understand, but what does Jesus mean by "hungering and thirsting after righteousness"?

Romans 4:4 Now to him that worketh is the reward not reckoned of grace, but of debt.

If I'm hungry and thirsty for righteousness, and I do work for the owner of the "righteousness store", then He owes me, and I'll be rewarded with some righteousness, right? Well, no.

Romans 4:5 But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness.

So when the Holy Spirit and my conscience get together and convict me of my sin; letting me know that I'm un-righteous (you all know the feeling), that's when I have a choice to make.

I can choose to ignore that feeling and wither away:

Proverbs 13:6 Righteousness keepeth [him that is] upright in the way: but wickedness overthroweth the sinner.

I can choose to do "good things", and try to make myself more righteous:

Proverbs 14:12 There is a way which seemeth right unto a man, but the end thereof [are] the ways of death.

Or, I can choose faith:

Romans 4:21-25 And (as Abraham,) being fully persuaded (having complete faith) that, what he (God) had promised, he (God) was able also to perform. (to bring forth life from the barren) And therefore it was imputed to him (Abraham) for righteousness. Now it was not written for his sake alone, that it was imputed to him; But for us also, to whom it shall be imputed, if we believe on him that raised up Jesus our Lord from the dead; Who was delivered for our offences, and was raised again for our justification.

As Jesus was being delivered for our offences, He indeed suffered physical hunger and thirst, but that's nothing compared to how He suffered as all our unrighteousness was poured on Him. Before He was delivered, He sweat as it were great drops of blood while seeking the Father's will (Luke 22:44). He prayed again and again for the cup to pass from Him; an angel even ministered to Him (Luke 22:43), but in the end, He set aside His own will, and by His faith was obedient all the way to the end. How precious is His righteousness! We cannot earn it; He doesn't owe it to us, but He promises it to us if we hunger and thirst after it.