When a plant is young, each time a new node appears, you'll see 2 leaves, each at the same height on the stem. These are called non-alternating.

As the plant matures, the leaves will begin coming out one at a time, staggered up each side of the main stem. This is when they are called alternating nodes.

Here are a couple pics to show the difference between alternating nodes and non-alternating.

First pic is non alternating, second pic shows alternating.