This is the 5th most frequent Japanese word.
て
"て" (te) is a particle used to connect verbs or phrases, the stem of a verb indicating sequence, or as a part of verb conjugation. It also means "hand" as a noun.
The word 'て' here connects the verb '読ん' and 'います' to form the progressive tense.
私は本を読んでいます。
I am reading a book.
The word 'て' is used to connect the action '話し' and the result '楽しかった', showing a cause-effect relationship.
友達と話して楽しかったです。
It was fun talking with my friend.
The word 'て' is used as a conjunction to indicate sequential actions between '洗う' and '食事をする'.