Stark many-body localization (MBL) occurs when interacting quantum particles are placed in a strong linear field gradient. Localization of excitations, coherent Bloch oscillations, Hilbert-space fragmentation, and scarring have been observed numerically and experimentally, but their origin is not understood. The authors explain these features analytically by perturbatively constructing an algebraic structure of Stark MBL Hamiltonians they name ``dynamical l-bits''. These structures are exponentially stable in the field gradient strength. Thus, the work has potential implications for quantum information processing.