In general, most, if not all of us will agree that wat's called the conscious mind is merely the surface phenomenon of an ongoing process that people usually refer to as the 'subconscious mind' (although I'd prefer the less ambitious term 'unconscious' or just 'not conscious'). The 'power' of this mind process (conscious or not) as a whole is evident and many scientific endeavours are actively trying to disentangle its properties and ontological status. Many findings have cleared definable questions about it, like which biological aspects of the brain appear to be related to which mental actvities or states. The end of this road is certainly not in sight yet, but yes, I'd agree that science is 'backing' the 'power' of this 'subconscious mind'.

J. Murphy's book The Power of Your Subconscious Mind, however, tries to extrapolate from the total amount of preliminary findings (ripe and green, as the Dutch expression goes) from these scientific endeavours, combining them with intuitions that go beyond what's really and definitely backed by science. Judging where it goes astray requires a reliable knowledge of all the scientific sources involved. For someone less well grounded, I'd advise approaching all such books, however inspiring, with a careful mix of trust and distrust. Well, that is the way to approach any publication, of course.