The twist boat conformation is more stable than the boat conformation of cyclohexane for a few reasons. The first reason is that in the twist boat conformation, all of the substituents are equatorial, while in the boat conformation, some are axial. Equatorial substituents are less sterically hindered than axial substituents, so the twist boat is less crowded and therefore more stable. Additionally, the twist boat has one fewer ring strain than the boat conformation - this also makes it more stable.
One other factor that contributes to the stability of the twistboat over the regular boat is that it minimizes 1,3-diaxial interactions. In cyclohexane, these interactions can be quite strong and lead to significant destabilization of the molecule. By adopting a twistboat configuration, these interactions are effectively eliminated.