Can there be an action free from the taint of desire? If there can be, what is the nature of that action? There must be a desire to even bring a glass of water to drink. Without desire, no movement is possible. First, there is a sensation of thirst; out of that thirst, there is the desire for drinking water. 

So, when desire is the fuel to carry out normal daily activities, what does it mean that Buddha didn't have desires? 

My guess is When there was a sensation of thirst, Buddha used to not identify himself with the sensation. In other words, there was an absence ego-identity with the thirst. But again, the desire to drink water, eat, move, etc. was arising. From where it was arising? 

Generalizing it better, the question turns up, Can there be an action free from the taint of desire? Because desires seem to be driving force of any action. Doesn't it? If there can be, what is the nature of that action?
Desire is a normal feeling thats why Buddha chose the middle way ,if you don't eat the desire to eat will definitely arise, its the identification with desire that poisons it as well as identification with any feeling or more accurately the attachment 

Explained well here 

Root of all things

.Thus effortless action is free from identification with desire .Its simple spontaneous and according to what the moment brings ,its not forced on oneself because with forcing the desire becomes identified with a person who wants to fulfill it, thus the attachment and suffering .When the desire arises and is simply known ,doing works on its own level.You can think of it in terms that desire is necessary just for action to  take place and not as a possessive mental state.

Notion of skillful desire

Also check this answer

Attainment of enlightenment without desire