Synergies are a feature in Diablo II introduced via patches. The general idea is that skills not only grow in power as players invest more and more skill points in them, but also enhance other skills of the same Skill Tree, mostly by increasing damage or some other stats.
Example is that a Sorceress putting skill points in Fire Bolt will also increase damage of her Fire Ball by 14% with each point, including the first. Note that only hard points (actual skill points put into the skill) add Synergy, not the skill bonuses from items.
Some synergies work two ways, that is, each point in Fire Ball will also increase the damage of Fire Bolt by 16%. The amounts given to each skill may or may not be same. Sometimes, upgrading a skill via Synergy may prove more effective than putting skill points in it. A good example of such skill is Bone Armor. Each point in this skill increase damage absorbed by 10 points, whereas its synergies by 15 points.
In a manner of speaking, this system allows the characters to increase the power of their skills far beyond the normal Level 20 limit (actual maximum of hard points in one skill). It also discourages more diversified, "hybrid" builds, as player needs to invest skill points not only in build's main skill, but also its synergies.
The Skills needed for the respective synergies can be seen at the very bottom of every skill's information in the Skill Tree.