Translation:Let me tell you a funny thing.
This is another example of the awkward Chinglish translations in these lessons. Perhaps "Let me tell you something funny" would be a bit better.
Yeah, quiet good example.
Cause in Chinese "let me" in this sentence is unnecessary. Also "tell" shouldn't be translated to "告訴", "說" is better. This sentence sounds like an elder is telling something serious to juniors. It makes something funny unfunny. We just say "(我)跟你說個好笑的(事)"
件 is a classifier for a number of different types of nouns, including 事情 ~ it's not limited to only items of clothing.
For that matter, 件 is not the catch-all classifier for clothing. For instance, the classifier for 裤子 (pants) is 条.