Okay so glycolysis happens in the cytosol, and the TCA happens inside the mitochondria. The NADH produced by glycolysis is impermeable to the mito membranes. So without a shuttling mechanism, the NADH that you make in glycolysis would not get into the mitochondria.
The malate aspartate shuttle allows for the NADH to transfer its reducing equivalents to inside the mitochondria.
It's actually a pretty cool mechanism because
no NADH is actually transported, rather, the electrons from NADH are moved inside the mitochondria to another, different NAD molecule by the interconversion of aspartate to malate on the outside and then malate to aspartate on the inside.
So, asparate -> malate outside the mitochondria, which is catalyzed by NADH -> NAD+, then the malate physically crosses the mito membrane. On the inside that malate is then converted back into asparate by the reverse reaction: Malate -> Aspartate, while using NAD as a cofactor creating NADH (inside mito).
So without actually making NADH cross the mito membrane, the reducing equivalents are still transferred to inside the mitochondria.
🙂
EDIT: Wiki has an entry on it with a good diagram -
http://en.wikipedia.org/wiki/Image:Malateaspartateshuttle.png