Literally, it is a request for a story. "I was almost hit by a car today." "Tell me about it." "I was crossing the street, when a car going 50 kph tried to make a right turn, and..." But it is often used in an ironic way. Irony can mean saying the exact opposite of what's really meant. In the ironic use, the word "TELL" is stressed. It means emphatic agreement. It means "you don't need to tell me about it, because it's a familiar problem. I already know a dozen stories like yours and I don't need to hear another." For example, "I hate Airline X. My flights are always delayed. This time we were three hours late getting out, and I missed my connection in Chicago." "Huh! TELL me about it. That airline is the worst. The flights are always delayed, and the food is awful, too."

By the way... I think it's unwise for English learners to try to use idioms. There are two likely problems when you use them. One is that many idioms have a specific pattern of accents, an intonation, a rhythm, a cadence that we expect to hear. If we don't hear it, we don't recognize the idiom. We don't sense irony. We assume the phrase means what it says. The second is that if you have even a slight accent, it is a little bit of work for listeners to listen "through" the accent. We have a little bit of trouble identifying your words. We do not expect to be hearing idioms, and we often do not recognize them when they are spoken with an accent. People think that using idioms will make them sound "like a native" and thus be understood more easily. In reality, until you are very advanced, and almost free from accent, the best strategy is to communicate using the most simple, direct, plain words and phrases possible. (A foreign speaker, once tried to tell me that something was securely fastened by using the idiom "It's not going anywhere." I didn't understand him because he said "It's not GOING anywhere," whereas a native speaker would have said "It's NOT going ANYwhere.")

It is called irony. Irony is when you say one thing but you mean another - usually the complete opposite. In this case, "tell me about it" means "no, you don't need to tell me anything about it, I already know". When you use irony, how you say the words - the tone - becomes very important, since that is your tool to indicate that you don't mean what you are saying. If you really would want them to tell you about it, you would be curious or even surprised. But you are not, since you already know it and you agree. Therefore, you must not sound surprised when you say it. You should sound like you have heard it before and you don't want to hear it again. Bored, with a sigh. Irony is easier to use with people you know. If they already know that you know, or they think that you know, it will be easier for them to understand that you mean something else. But irony is an advanced feature in a language, I suggest that you say things like "so do I" or "I agree" in order to not be misunderstood. And listen closely to the tone they use in the movies, when they say things they don't really mean.

In this context, it just means, tell me more details or tell me the whole story of what happened. In other contexts, depending on the tone of voice (or as Ingo said, if accompanied by a sigh), it just means you agree with another person's negative statement or judgment about something (A: This class is really hard! B: Tell me about it. I've received an "F" on the last three tests!) BTW, 你的猫很可爱。

This probably is a problem of pronunciation. If you say it like a question then people will surely answer your question. However, if it more sounds like a *sigh* and not like question people will understand that is more of a rhetorical question.