For Crown Law guide, go here: Crown Law (guide)
Investiture laws is a small set of laws that only apply to Catholics; no other religions will have it. Investiture law decides if the Pope appoints bishops, or if their liege does. This means that if you have Papal Investiture you will be unable to affect who your bishops are.
If you've got Free Investiture you'll be able to appoint the successor to any bishopric that is your direct vassal, and every subject within your de jure kingdom will be able to do the same. This makes vassal bishops considerably happier with their lieges, as they are grateful for having been appointment, and they therefore get +25 opinion with whoever their liege is. Any vassal you have that himself has bishops as vassals will also be happy with you, as he now has control over his bishops. You'll thus get +10 opinion with most of your vassals.
However, the Pope will be quite unhappy with this state of affairs. You will get -30 opinion with the Pope making you much more vulnerable to excommunication. In addition, every time a new king gets the throne the Pope will request, generally within a few years, that the investiture laws are changed to Papal Investiture, which will give you the option to comply (which will raise the moral authority of the Church by 2%), refuse (reduces MA by 2%), bribe the Pope (costs 200 gold), or if you have a Learning skill of 16+, refuse on theological grounds (gives you 1 piety).
This means that over time, Free Investiture does have the potential to be a moderate money drain over time. However, as long as your realm is moderately large, the gold needed for a single Papal bribe is unlikely to be more than a couple year's income at most. The largest disadvantage to Free Investiture is the much increased risk of excommunication, and as long as you have political enemies and a lack of traits the Church likes, you can easily end up excommunicated, giving every Catholic in the world a casus belli against you, and reducing all your vassals' opinion of you by 30.
However, Free Investiture is still generally preferable over Papal Investiture due to the boosts to vassal opinion. 10 opinion with your nobles can at times make the difference between rebellion and loyalty, and the 25 opinion with bishops makes their taxes much more likely to go to you than the Pope.