This is both a good and common question that unfortunately comes up because so many learning resources seem to treat it as a "you shouldn't use this", but that is far from the truth.
So, let's look at what it is: it could be one of two things: introducing you as the topic (and possibly implying that you are the subject), or acting as a contrast.
The first one is much more common. Let's take a simple sentence
日本語を勉強しています。（にほんご を べんきょうしています。) "(someone) is studying Japanese."
If you were to start a conversation with this sentence, you'd definitely get some strange looks. The topic of the conversation hasn't yet been announced, so there is a bit of a jump to presume that you, who are speaking, is the person studying Japanese. It's somewhat jarring.
So, if you are saying "hey, let's start the conversation by talking about me", or "I'm changing the conversation from something else to me", you'd preface this with 私は.
Now, this is not a 100% rule - there are some utterances you can make out of the blue (like おなかがすいた so say you're hungry) and everyone will presume you are talking about yourself), but this should be something you aim to do when the topic of the conversation shifts.
The reason it is often noted as a "you should omit this" is, if you have already been established as the topic of the conversation, there is no need to keep saying 私は after the first time. We most often hear this mentioned for self-introductions. You might use 私は to introduce your name, then drop it when talking about where you are from, etc.
So, to summarize, there is not a "you *should* drop 私は" rule until you look at the timing and context of when it might be said.
Contrastive は
There is one more usage of は, sometimes called the contrastive form. This rarely comes at the beginning of the sentence, but tends to be in those strange-looking "double は" sentences like this.
今日は 私は 学校に行きます。 (きょうは わたしは がっこうにいきます). As for me, I am going to school today.
The first は marks the topic (today). The second one is dropping "I" i n there as a contrast to something else that was said earlier in the conversation. Perhaps the other person said that they are going to the park today, school tomorrow. You say, "Well, **I** am going to school today." In that sense, the は is not a second topic particle, but a way to draw contrast with the other sentence.
