Support simply means that you give evidence to prove your point is true. Support must be given at all levels: the thesis statement must be supported by your topic sentences; your topic sentences must be supported by your major supporting details; and your major supporting details must be supported by your minor supporting details. And your minor supporting details must be very detailed and specific, making it perfectly clear to the reader that there are good examples and explanations to show that each point in your essay is true and so your main point is also true.
An important aspect of support is that it must be detailed, believable, expressive, and true.
Your support must be detailed: you cannot simply say that the Chuo Line is overcrowded "because many people ride the train." That's not enough. You have to "paint the picture," make the reader feel how crowded it is. Describe a Chuo Line train car at rush hour, how station workers have to shove people into doors crammed full of people. Describe standing in a sardine-can train with oily-haired businessmen and an old bad guy with bad breath squeezed so tight that you can feel the old guy's sweat through his shirt, and the businessman's umbrella is stuck in the heel of your shoe and his briefcase is poking your stomach, and when the train stops, they all fall on top of you.
Your support must be believable. Don't write about facts which are so incredible that people will think you just imagined them, even if they are true. Make sure that your reader can accept the stories; if not, you are just hurting your essay. For example, true story:
One night at home, I came down to dinner and my wife asked who I was talking to on Skype. I told her I had been completely silent, and there was no one talking upstairs. She insisted that she clearly heard a voice through the ceiling—she couldn't understand any words—and thought it was me. Five minutes later, the phone rang: it was her brother, reporting that their father had just died.
Told factually, readers can perhaps barely accept such a fantastic story, because it is told objectively. However, if I told the same story with references to ghosts and the spirit world, and claimed my wife was psychic, many readers would think that I was making the whole thing up, or that I was not reliable as a witness. Make sure that you give the facts in a way the persuades the reader. (...and yes, the story is true; it happened in late June, 2011.)
Another example comes from a student's essay, when the student wrote about a crazy bus driver. He wrote about the driver going over 80 kph on a city road, about an old lady being knocked down, and about how everybody on the bus was screaming. The student sincerely insisted that the story was true—but the way he told it, it sounded too fantastic to be accurate.
Think about how your audience, people who did not share the experience, will consider it.
Your support must be expressive: it must be told in a way that makes the reader feel strongly about your point. If possible, evoke emotions; try to make your reader upset, or excited, or amused, or angry. Don't just write, "many people have problems with family members"; your reader knows this, but cannot feel anything about it without expressive details.
Instead, tell the story of the 40-year-old woman, too busy for a life or family of her own, who works 60-hour weeks to support her parents, only to come home and find that her invalid mother has not been fed or cleaned all day, while her lazy father was at the pachinko parlor all day, wasting the little money they had for food and electric bills. Then make your point about how social systems have to be improved to help poor people with elderly parents.
Finally, your support must be true. Many students guess at facts, or even make them up. You cannot do this. Everything you write must be fact. You should not write something that you are not sure about. Perhaps you are writing about modern diets, and you mention that diet soft drinks are unhealthy because their chemicals hurt the stomach. It sounds true, and maybe you "heard about that" from a friend... but is it really true? If so, there should be a scientific study, or a report from a respected source. Without such a source, it's just a story. Your facts should be ones you know are true, not ones you think are true. Be careful about what you claim.