A tailor helps make your clothes fit you better. Similarly, when you tailor something to the needs of others, you are adjusting what you do to best suit them rather than taking a general approach.
The word tailor comes from the Latin taliare, meaning "to cut." A tailor is someone who cuts and adjusts your clothing to better fit. When you tailor a jacket, you have it taken in to better suit your physique. But tailor isn't used strictly in reference to clothing. For example, a restaurant might tailor an order for a vegetarian by getting rid of the meat in a portion. A teacher might tailor a lesson plan to the demands of her ESL students.