Clarification: 開く is an intransitive verb. 開ける is a transitive verb. Transitive verbs require a direct object to complete their meaning whereas intransitive verbs do not. In English, many verbs can be either in any given sentence.For example, "Mr. Smith boiled some water." Boiled is transitive."Mr. Smith’s water boiled." Boiled in intransitive.Here are some example sentences in Japanese: ドアが開きました。"The door opened." Intransitive.スミスさんがドアを開けました。 "Mr. Smith opened the door." Transitive. Hopefully that made the difference between the two clear. An extensive list of other transitive/intransitive pairs can be found here. Please feel free to ask questions or correct any mistakes that may have been made.

Clarification: 開く is an intransitive verb. 開ける is a transitive verb. Transitive verbs require a direct object to complete their meaning whereas intransitive verbs do not. In English, many verbs can be either in any given sentence.

For example,
"Mr. Smith boiled some water." Boiled is transitive.
"Mr. Smith’s water boiled." Boiled in intransitive.

Here are some example sentences in Japanese:
 ドアが開きました。"The door opened." Intransitive.
スミスさんがドアを開けました。 "Mr. Smith opened the door." Transitive. 

Hopefully that made the difference between the two clear. An extensive list of other transitive/intransitive pairs can be found here. Please feel free to ask questions or correct any mistakes that may have been made.