This is when someone draws a conclusion with only a little bit of information, and/or time. Here's one example:

This pooch made the assumption that he was a cat in a hasty manner, he only looked at the number of his legs. Based on his logic, he is also a giraffe.

Suppose we went to Florida for several days, and the weather was unusually chilly. After returning home, we conclude that Florida is quite cold. This is a hasty generalization because the weather we experienced was atypical. So to generalize from such little information is a fallacy.

One more example: "Joe is a creationist, and his research is very sloppy and poorly documented. Therefore, creationists are bad researchers." The fact that maybe one creationist is sloppier than an atheist does not make every creationists bad researchers.

Basically, hasty generalization is just jumping to a conclusion way to soon.