What does washing and drying a solution mean?
This is standard for purifying substances.
To wash means to add your product solution to an aqueous solution (or just water, but frequently a saturated solution) to a separatory funnel. After shaking, you drain the lower layer (which is usually aqueous). This process removes water soluble impurities. This is frequently repeated.
Drying is accomplished by taking the organic solution of your product and mixing it with a desiccant (usually anhydrous sodium sulfate or anhydrous magnesium sulfate). This removes any water that was left from the washing in the above step. The desiccant may then be removed by filtration.