Mining involves harvesting resources from asteroids, either in asteroid belts or special mining signatures located via scanning.
If you decide to pursue mining as a source of income, you’ll probably want to use a Venture, as it is the best dedicated mining ship you have available as an alpha clone. Its 5000 m^3 Ore Hold allows it to store a significant amount of ore so that you don’t have to return to a station to drop off your ore quite as often.
It’s relatievly easy to sell the ore you mine, though the profits may be relatively low for highsec miners. Mining in lower security space can increase profits but also increases the level of risk, as players may frequently try to attack you.
You can read more about mining in the UniWiki ‘Mining’ article.
Mining is probably the most sedate of all EVE income opportunities - once your mining lasers are activated on an asteroid, it’s mostly just waiting for the raw ore to come streaming in. If you’re mostly interested in socializing with other players, it can be a great activity to do while socializing.