I am a student. I want to go to Canada and visit for a couple of months and then go home. What should I write in the "Purpose of Travel" section? Could you give me some successful samples?
If you look at the information provided by the visa application form (and see that linked question for more information), you'll see that it suggests you supply a copy of a flight ticket showing you will depart Canada (do not buy a nonrefundable ticket or make nonrefundable hotel reservations before you have your visa) or a travel itinerary. In other words, they aren't just looking for a one word answer like "tourism"; they want documentation of your plans.
So you could type up a document stating that you plan to visit Canada for tourism purposes, and then supply your itinerary and accommodation plans: where you will go, when you'll go there, where you'll stay, how you'll get from place to place, etc...
Note that the question specifically says "You must submit proof that you are coming to Canada for a temporary visit." This is your opportunity to convince the officials that you will leave Canada as promised. So somewhere in your application, you will want to ensure you supply proof that you are a student, will be enrolled in classes after you return home, and other documents that show strong ties to your home so you can demonstrate that you will not overstay.
Although you're a student in your home country, you want to visit Canada for several months, so it would be as a tourist.
The Government of Canada web site will guide you. It takes you step-by-step through the process, telling you what type of visa, what documents, and what arrangements are required.