Originally just for Twitter, the term "hashtag" (also known by the symbol #) has migrated to phone texting as well. A hashtag is used to group a topic of discussion together.
A hashtag is a way for someone to write something on a topic without directly including it in the sentence. There must be words with the hashtag; a hashtag can never exist on its own. For example, if someone was to text a sentence that said, "Outside waiting for Uber for 30 minutes," he might hashtag it #annoyed or #areyoukiddingme. While hashtag is understandably popular on social media because it helps use search functions better, there is no real reason to use it in texting other than to give strong emphasis to a statement.