This gets straight to the point, laying out your argument from the start without any accoutrements or stylistic word play. For example, you could begin your essay, "The application of the death penalty in the United States has been marred by racial and socioeconomic bias." By setting up your essay this way, you let the reader know immediately both what the essay is about and what argument you'll be presenting.
An interesting quote related to your subject matter is one way to get your readers' attention from the start. For example, you could begin with this statement from former California governor Pat Brown, "The most glaring weakness is that no matter how efficient and fair the [death penalty] may seem in theory, in actual practice it is primarily inflicted upon the weak, the poor, the ignorant and minorities." Such a quote brings your reader directly to the heart of the argument that you are about to make and sets the tone for the remainder of your essay.
Another way to grab your reader's interest is with a compelling statistic or series of statistics offering a window into the case you are presenting. With any topic, a startling statistic that gets right to the heart of your case will make your readers sit up and take notice. In an analytical essay, you will be arguing with data, not merely opinion, so you can lead readers to your thesis statement with a grounding in fact, and lend weight and credibility to your essay from the get-go by using verifiable numbers.
You could also engage your readers with a dramatic scene. By giving readers an evocative scene, one they can picture in their mind's eye, you make the topic real and relatable to them, while at the same time buttressing your case with events that actually happened. This engages them on a visceral level, which makes your thesis statement all the more poignant.