Well, welcome new person to the game.
SO = Single Origin enhancement (Like Science or Mutation)
DO = Dual-Origin enhancement (Like Science/Tech or Natural/Magic)
DO's will provide a lesser bonus to your stats than SO's. Further along, generally around 35, players will slot IO's (Invention Origin enhancements) that are craftable at the university or in a base. There are Set enhancements that are also IO's, but provide further bonuses depending on how many you slot into a particular power.
Once you hit level 10 you should get a contact at the university in Steel Canyon, which will lead you through the steps for crafting a generic IO.
Keeping enhancements leveled up gets expensive at the higher levels. The Homecoming devs were kind enough to provide us with a 1-buttong click to upgrade all of our enhancements (DO's/SO's) in one shot, but it'll cost. My Corruptor ding'd to 47 tonight and all her SO's turned red (which means they are too low to provide any bonus) and it cost a little over 5m influence to update them all. In the grand scheme of thing that's not that much, but I don't marketeer on all of my characters so their pockets are generally not overflowing. :)