Letter grades are simple and, generally, universally understood. Using the letters "A" through "F" to grade students is known throughout the world and sets a simple and accessible standard. Grades can be assigned quickly using letter grades and can be sorted in broad categories for student evaluation or other purposes.
Letter grades represent a broader range than percentage point but aren't as broad as pass/fail. While it may be difficult to tell the difference between 74 percent and a 76 percent, it is easier to tell the difference between an "A" and a "B" paper -- especially if criteria are set out in a rubric or elsewhere. By providing a range within the letter grade, the effects of small errors in judgment by the grader -- say, over- or undergrading by a few percentage points -- are eliminated.
Letter grades allow for more maneuverability that some might think. By allowing for "+" or "-" in letter grades, scores can be more or less nuanced depending on the situation. Again, this is not as precise as percentage points, but it is not as imprecise as pass/fail. When using letter grades, evaluators can also set the pass/fail bar wherever they please -- for instance, "F" could be a failing grade but so could "D."
Letter grades may also force evaluators to provide greater justification for their grades. While a percentage score seems precise, it may be just as imprecise as any other form of grading, especially if the test or assignment is not true/false or multiple-choice based. Letter grades, when combined with thorough evaluation notes, may be thorough and helpful to students.