Mostly it has to do with the feeling of the outcome. Intervene is used to describe an act that has a positive outcome. Interfere is used to describe an act that has a negative outcome. I intervened in my friends' fight. <-- I tried to stop them from fighting. I interfered in my friend's work. <-- I interrupted his work.

Both refer to inserting yourself into an interaction between others, without being invited. To "interfere" is destructive. You are not trying to be helpful. You are trying to block something constructive, or trying to turn it to your own advantage. For example, a father does not approve of his daughter's boyfriend and says he will cut off her allowance if she doesn't break up with him. He is interfering with their romance. "Interfere" can be a synonym for "meddle" or "intrude." We also speak of physical interference. For example, "I can't get good reception of a weak TV station 50 km. away, because there is interference from a strong TV station 5 km. away." To "intervene" means to put yourself in between two other parties, usually in order to be helpful. If you are trying to stop something, you are trying to stop something harmful. For example, if two people are arguing and look like they might be about to fight, and you step in between the two and say "Just cool down for a second and let's talk about this," you are intervening. Intervening can be a synonym for "mediation."

They mean the same thing, but have slightly different connotations. "Intervene" has a slightly positive connotation, and "interfere" has a slightly negative connotation. Examples: "His son was nearly kidnapped, but a nearby stranger intervened at the last second." "They were about to go on their first date, until the boy's father interfered." In the first example, the stranger is preventing a kidnapping, so you'd more likely hear "intervened". In the second example, we're probably cheering for the kids going on a date, and are disappointed that the father stopped the date, so we're more likely to say "intefered".