A $P$-invariant subspace is $T$-invariant, hence it is a sum of weight spaces. So, each such subspace corresponds to a subset of the set of positive roots. The additional condition of $U$-invariance forces these subsets to have the following property: if $\alpha$ is in subset and $\beta - \alpha$ is a sum of positive roots then $\beta$ is in the subset.
EDIt: All this is for the case $P = B$. For arbitrary parabolic the situation is more complicated, see robot's answer.