Apoplast:

The term apoplast was coined in 1930 by Munch in order to separate the living symplast from the dead apoplast.
The apoplast is the space outside the plasma membrane within which material can disperse freely. It is broken up by the Casparian strip in roots, by air spaces between plant cells and by the plant cuticle.
The apoplast route facilitates the transportation of water and solutes across a tissue or organ. This process is called apoplastic transport.

Symplast:

The symplast is the inner side of the plasma membrane in which the water and low-molecular- weight solutes can freely diffuse. Symplast cells have more than one nucleus. The water enters the cytoplasm of the cell all the way through the plasma membrane; hence, the symplastic pathway should cross cell membranes. Since the symplastic pathway crosses the cell membrane, it is also called transmembrane pathway. The movement of water in the symplastic pathway is assisted by cytoplasmic streaming.