A college entrance essay for a student with less than stellar grades can be the deciding factor, along with letters of recommendation, as to whether she is accepted. Conversely, a student with adequate grades and letters or recommendation who delivers a poor essay may lose a spot to a student with weaker grades but a strong essay. This is a bit unfair, since the student who did badly on the essay might have just had a bad day.
Think of a college essay as a way to not only introduce yourself. When applying to a bachelor's of arts or science program it is normally the general college that reviews your application. In graduate school it is the head of the program that you are applying to or those within the department that have been asked to participate in reviewing applicants, like the vice chair of the department. One of the pros of a strong essay in a graduate program, for example, is that it can put you in good stead with the head of your program.
One "con" of writing and then submitting a college essay is that it tends to cause many applicants quite a bit of stress as he or she awaits an admission's decision. If a student felt that other factors were might important, the process might be less stressful. This is also one of the reasons why it is important to apply to more than one college so that you don't place all your hope of going to college in one institution's decision.
Another "pro" of writing a college essay is that through the process of developing your essay you are given a chance to truly define your academic goals in a way that you may not have thus far. It is often helpful to think about what matters most to you and how this fits with the career path you have chosen. If you haven't selected a field to pursue yet, it is a good idea to write about your motivations for choosing to go to college, such as wanting to help others or your desire to have a positive impact on the world, perhaps linking these goals to personal experiences.