Billboards build trust. The more often people see a message in different locations and environments, the more they are convinced it is a genuine business with a quality product.
Repetition is the key. You will be familiar with positive affirmations to build your self-confidence. Imagine I kept telling you (for example) butter was better for you than margarine, every time we spoke?
People go through various stages of resistance, from being aware you are advertising to them (and consciously blocking it out), to being aware and ignoring it, to eventually letting it in and starting to be influenced by it.
When you create your digital marketing strategy, consider the overall message you are sending, check it for consistency across the platforms, and most importantly, put it in all the places your prospective customers are going to be.