Foods in this game are used to increase attributes and sync rate. The effect on sync rate happens straight away but he effect on attributes isn't immediate however, only then character has fully digested the food do they gain the attributes from the food.
Food is digested after a number of battles have been won. At the top right of the description box it will say goes down in X bytes. X is the number of battles you need to win.
For example, to gain the +40 HP effect and fully digest a Rolly Jelly Q10 it will say goes down in 20 bytes, meaning you need to win 20 battles for this to happen.