The water is attracted to the point of the needle. The meniscus goes up from the water sticking to the point.
When water molecules stick to other molecules like little magnets its called "molecular adhesion." This explains why a paper towel cleans up spilled water easily: the water molecule acts like a little magnet and sticks to the polar surface of the cellulose, which also has a magnetic attraction for water. A water molecule will stick to any other polar molecule, but not to non-polar molecules like oil. That is why oil and water don't mix.