What's the difference between these? I know that both of them, refer to something becoming another state in some sense. Dankon.

Correction -ig- versus -iĝ- - my mistake!

Welcome to the wonderful world of verb construction in E-o!

-igi denotes, that someone or something makes a thing to happen
-iĝi denotes, that someone or something becomes something

In the later case it's about reflexive verbs. Now depending on your native language the difference might be hard to grasp. For instance English usually doesn't even denote this difference:

• "You open the door" : you make the door open
  
• "The door opens" : some unspecified force makes the door open; later it can be turned out, that it was a person, wind or...

If we now translate those sentences,

• "You open the door" : Vi malfermas la pordon
  
• "The door opens" : La pordo malfermiĝas

you may wonder, why in the first case the verb doesn't have -igi-ending despite you making a thing (the opening) to happen. The reason is, that the word root ferm has a verbal word character (vortokaraktero), i.e. it already denotes an action, thus fermigi would be superfluous. Other possibilities are noun-like and adjectival characters. That's why the verb fermi is the first in a dictionary like PIV.

In general you may form both -igi and -iĝi forms only from adjectival root (as well as the -i form):

• La cielo bluas : The sky is blue.
  
• Mi bluigas akvon : I make the water blue (e.g. by using a chemical that turns it blue)
  
• Miaj lipoj bluiĝas : My lips turn blue (e.g. it is so cold)

See a longer discussion here in Lernu.

Thank you. I'm still trying to get my head around this. The concept makes sense, but it doesn't come naturally to an English speaker.

Part of the reason has to do with causation versus becoming.
The tree falls. {non-causitive}
He felled the tree. {He caused the tree to fall.}
He rises at six o'clock. {non-causitive}
He raised her (up). {He caused her to rise.}
The pages have yellowed with age. {They became yellow — there might be a chemical cause, but the verb "to yellow" {in this specific example sentence} does not indicate cause, it only indicates becoming.}
I've reddened the wood to give it … {I've caused the wood to take on a red hue.}
Languages like Japanese have causation built into them, and Esperanto is similar. So you can indicate causation or becoming {non-causitive} thus:
-igi = causation, e.g., ruĝigi = to cause to become red, or to make red, to redden
-iĝi = becoming, e.g., ruĝiĝi = to become red, turn red, such as leaves {In English, there is no distinction between causation with colours, so that we can also say, the leaves have reddened.}
-i = {in the case of colours, to be a certain colour}, e.g., ruĝi = to be red

In addition, non-causitive verbs are intransitive {they do not take an object, such as the leaves or the yellowing pages}, whereas causitive verbs are transitive, i.e., someone causes something to happen to something, such as the wood I reddened.}