Start with the understanding that nobody truly "reads" anymore. Since it is an essay, you probably don't want to use bullet points, but, dang near! Make it easy for them to scan it and get the key points. How?
Begin with your conclusion: pack a punch (I learned this in legal writing!) Example: " I think the death penalty should be abolished because too many innocent people are executed, it disproportionately impacts the poor and minorities, it is costly for society to prosecute and defend the accused, and it does nothing to deter others from committing crimes." You would then have a paragraph on each point, with the first sentence of each paragraph also packing a punch, and end with a conclusion which is a restatement of your main points.
If you cannot think at a keyboard, please use paper and pen! Scribble down your thoughts. Don't worry about getting the wording right, getting them in order, or anything like that, just capture them before they slip away. You can always clean it up later. Make sure you read and re-read what the school wants the statement to say. Remember it is not all about you. Don't get too mushy with it, but, you have a gift, and you want to contribute to society - however you want to say that! You may want to hit on your ability to meet your goals, how you have planned to be able to do that, you have nothing else standing in your way of completing the program, etc etc.
Might not hurt to run it by a professor!
Hope this helps!