The umbrella is an interesting tattoo design. At its most basic level, an umbrella is a symbol, or symbolic, of a temporary shelter, or a small amount of protection. Umbrella itself, literally means, a little shade.
If you're a Buddhist, the protective force, or shelter, is the dharma, the Buddha's teaching, the faith. Depictions of the Buddha often show him protected from above by an elaborate parasol. The dome symbolizes wisdom, and the hanging skirt, compassion. The Noble Eightfold Path found representation in octagonal parasols.
In modern popular literature, the umbrella often becomes a vehicle to transport an individual, and in this respect a tattoo design of an umbrella is similar to tattoo symbols like wings. Think of Mary Poppins, carried aloft on her 'magic' umbrella, and spirited away to a new adventure. In stories, umbrellas are often used as surrogates for parachutes, in which an individual takes a 'leap of faith', either from great heights or into the unknown, and the umbrella acts to help gently guide the protagonist to the next step on their journey of discovery.