Interfere has a negative connotation; it is when someone/something affects a situation, and you don't want it to:
I wish my mother would stop interfering in my life!
I'm trying to study, but the noise is interfering with my ability to concentrate.
Intervene has a more positive connotation; it is when someone/something affects a situation in a good way. We often use it for stepping into a conflict or argument to prevent it from getting worse.
Bob and Joe were about to start fighting, but Pam intervened and calmed them down.
The diplomats intervened in the conflict and negotiated a peace agreement between the two countries.
The same is true for the noun forms: interference and intervention.
The citizens are angry about the government's interference in the economy; there are so many rules and regulations that it harms businesses.
(interference = negative connotation)
The citizens are happy about the government's intervention in the economy; the new laws and incentives have saved the country from a crisis.