The progressive tense shows an action in progress, ongoing and not finished. It is also called the continuous tense; both names mean the same thing.
It is built from a form of be plus the -ing form of the main verb: She is writing a letter right now. The engine is running while we wait.
How it looks in sentences
They are running now. The picture is one of motion caught midstride, not a general fact about them.
Dora was walking on the beach. Here the action was under way at some moment in the past. The same be-plus-ing pattern shifts to whatever time you mean: Ryan will be going to the gym points ahead, I am playing football now points to the present.
Not the same as the simple present
A common slip is dropping the be verb: I eating dinner is incorrect, while I am eating dinner is correct. The be form is what marks the tense, and the -ing word alone cannot do that job.
Watch the contrast with the simple present: I am eating dinner points to an action happening as you speak, while I eat dinner would describe a habit, something you do regularly.