From OpenCog

A type of Link which defines a Hebbian connection that works in both directions. Slightly mysterious, since the default HebbianLink is also symmetrical.

Hebbian links connote associations between their arguments, i.e. they connote that the entities represented by the two arguments occurred in the same situation or context, for instance:

HebbianLink happy smiling

The symmetric aspect defines that the association goes in both directions. When observing 'happy', 'smiling' is often also observed and vice versa.