To be keen to do something means you like to do something. Ex. He is keen to learn English He likes to learn English. To mean to means that is the plan. Ex I mean to visit him today. I plan to visit him today. To insist on means you tell someone to do something and you will not takke no for an answer. Ex. I insist on your doing your homework outside of my class. Hope that helps! John

Usually, you hear the terms as such - keen on, mean to, insist that. To be keen on doing something means you are both eager and interested in doing something. A sense of dedication can be conveyed as if one will not stop until they have attained something. Ex: He is keen on finding someone to teach him the process. This can mean, he is both eager and interested in finding someone to teach him the process. There is an insinuation that he is dedicated to finding someone who will teach him this process. To mean to means you plan or intend to do something. Usually you hear this in the past tense. I have never heard "mean to" in the present. Most often, it insinuates that something occurred causing you not to complete the action. Ex: I meant to visit my brother today, but I became extremely busy and forgot. To insist on something means that you demand something and refuse otherwise. Usually, it is said in the context of something being feasible. The word carries a welcoming connotation. Ex: I insist that you stay the night with my family. Really, it is no bother. Here, you are saying that the person staying with your family does not cause an inconvenience. Moreover, they are welcomed into your home without question. I hope this helps! As with many words in English, the meaning can vary depending on context. I gave you the most common and everyday usage of the terms. Good luck!

Both Breonte's and Johnz's answers are good, but there are some extra nuances of meaning. There is a very slight difference between 'keen to' and 'keen on'. 'Keen to' is more often used to express your willingness or desire to do something. It is used together with the infinitive of a verb. It also implies eagerness and/or optimism. Compare: "I want to learn English", "I am keen to learn English". In the first example, there is no inference of any emotional state. The second example ('keen to') suggests that the speaker is excited and happy about this activity. 'Keen on' is more often used to express that you like something. This is used together with a present participle of a verb. Again, it implies slightly stronger feeling. Compare: "I like running", "I am keen on running". In the second example, it sounds as if the speaker likes the activity ever so slightly more. There is also a very weak inference that the activity is more regular. 'Keen on' can also be used about objects or people. It is unusual to use it to describe your feelings towards an object, and using it about a person implies the early stages of romantic feeling. If you were to say, "I am keen on Suzanne" then it sounds as if you are planning on taking Suzanne on a date! Again, both Breonte and Johnz are entirely correct about the use of 'mean to', but there is a little more nuance of meaning. The past tense usage is more normal, as Breonte said: "I meant to do that" meaning "I intended to do that", "I did that deliberately". 'Mean to' can be used in the present tense to show your intention to do something in the future. This could be at any point in the future. All of these are acceptable: "I mean to beat you in this game of tennis", "I mean to visit him tomorrow", "I mean to visit England this year". Using 'mean to' in this way is slightly less usual, and raises class implications (in British English - I don't know about American English). It would more usually be used by upper-middle-cl