Black mangrove trees do not develop stilt roots the way that red mangroves (Rhizophora mangle) do, but they do grow these pneumatophores.
Pneumatophores probably help the mangrove trees to improve oxygen uptake in strongly anoxic substrates. Cypress knees are believed to have a similar function.
It takes a while for the pneumatophores to develop. I only began to see them a few months ago on my plants, but I have been growing them in riparium planters for a couple of years.