Te-form is very important because there are so many other grammer points that use the te-form! For example, if I want to say I'm doing something now, then I need to use the present progressive tense. In Japanese, this uses Te-form. First you conjugate the verb to Te-form, then you add -imasu (or add -iru for a casual conversation).
E.g. I am doing it now.
In Japanese, the verb to do is する (suru), or します (shimasu) in -masu form. So I conjugate it to -te form first. する is an irregular verb and has the te-form of して. Thus, the present progressive would be しています (or している) casually.
If we add in the extra vocabulary we need of 今 (ima -> now), 私 (watashi -> I), は (wa -> signifies the topic), then we can make this sentence. The full Japanese sentence for this example would be: 今、私はしています。
It might be more common for the subject to be implied though, so you might hear 「今しています。」 or 「今している。」
There are many grammar points like this! For example, the short form past tense uses the same rules as te-form, but using ta instead. For example, the short past tense of する (suru -> to do) is した (shita). Or you can ask for permission by using te-form with ~もいいですか? Once you master te-form, you will be able to easily learn new grammar points and the world of sentences you can make in Japanese will begin to open up!
I learned te-form through songs when I first started, and that really helped me! Here are some that I like:
- https://www.youtube.com/watch?v=uW1YcozsWh4
- https://www.youtube.com/watch?v=4BEnw7J6hiw
- https://www.youtube.com/watch?v=hkO1jCuhWOw