A corporation is a player run group, similar to a guild. What you might get out of one will vary wildly, depending on its members. For some it is a tax haven. For some it is used only for the organization extra hanger divisions provide. Others use it to gather people of like mind, either PvP or Industrial, and organize them into a more effective force. A corporation is required for owning Upwell stations, and that can be important to some. Corporations can join alliances, participate in wars as the aggressor or defender if they own upwells, or just take pride in the flag they fly. The permutations are as limitless as the minds that can come up with them.
Factions, though, generally refers to the NPC factions of the Eve universe. There are 4 Empire factions, and there are Pirate factions. Empire factions are the Gallente, Minmatar, Amarr, and Caldari. You have standings towards these factions and the NPCs who hand out missions will likely belong to one of these factions (Or the Sisters of Eve, an independent faction, but I digress).
There’s a more indepth guide that was well received here:
It is a bit dated, but since it’s mostly a social construct and people haven’t changed a whole lot, it should still be largely valid. My personal advice is to group up with people you find who are of like mind. If corporations are not a thing you’re ready to commit to, many will have public channels to hang out in so you can take them for a test drive, or you can start a channel of your own and make some Eve friends from scratch, too, if you would care to. You want to find a balance between being over cautious and remaining isolated and falling in with the wrong crowd, or a corporation looking to exploit you.
I wish you well, Capsuleer. Fly safe.