限りだ expresses the speaker's feeling that something is at an extreme level, often equivalent to “I feel extremely...” or “it is extremely...”. It commonly follows an evaluative i-adjective, a na-adjective with な, or a noun with の. The construction is especially common in formal statements of gratitude, honor, happiness, regret, or admiration, and it often conveys a strong, sincere emotional reaction rather than a neutral measurement of degree.