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Dripping refers to the technique of removing the cap or drip tip from a dripping atomizer (called an RDA, just a barebones atomizer, no tank or reservoir) and manually dripping ejuice directly onto the wick/coil until saturated, then vaping it nearly dry.
This provides a much more robust and intense vape, vastly customizable to your particular taste, enabling you to get the most flavor and vapor out of your juice. The downside is that it's labor-intensive, it can only hold a few drop of juice before it dries out and gives you a nasty dry hit for your trouble. It also comes with a learning curve in building it so it works not only properly, but at it's best performance.
Then there are rebuildable atomizers (RBA) that have a small tank for juice and work in a similar fashion to the clearomizers you may already be familiar with. They combine the best of both worlds, the convenience of juice storage for hands-free vaping, with the intensity of a customizable atomizer.
You can run one on an eGo, but the battery's lack of power and built-in circuit protections limit your build options and won't provide the intensity that justifies the effort with an RDA/RBA. If you choose to explore this option, a mod upgrade is required. Plenty of mods are available that provide the safety of an eGo while still giving you the power you need to take advantage of advanced attys.
Mechanical mods have no circuit protection and are used for sub-ohm builds. Sub-ohm gives the most intense vape, but there are increased risks with it. Advanced knowledge and experience is required to safely manage the abusive use to which sub-ohm subjects batteries to. Best not to mess with that for a while.