Learn Spanish (Latin America): El jefe está leyendo el periódico.

The verb is leer (to read). Usually, to make the "-ing" form (the gerund) for an -er verb, you drop the ending and add -iendo. But if we did that here, we would get leiendo. In Spanish spelling, an unstressed 'i' between two vowels changes to a 'y' to make it easier to say. So, it becomes leyendo.

Why do we use está instead of es for "is" in this sentence?

To talk about an action happening right now, you always use the verb estar (to be) plus the gerund (the "-ing" word, like leyendo). The other verb for "to be", ser (which es belongs to), is used for things like descriptions, identity, or time, but never for actions in progress.

Could I just say El jefe lee el periódico instead?

Yes! In Spanish, the simple present tense (lee) can mean both "he reads" generally and "he is reading" right now. However, using the present continuous form (está leyendo) puts a spotlight on the fact that he is in the middle of doing it at this exact moment.

Why does the word periódico have an accent mark on the 'o'?

The accent mark tells you which syllable to stress when speaking. By default, Spanish words that end in a vowel, 'n', or 's' naturally stress the second-to-last syllable (pe-rio-DI-co). Because the emphasis actually belongs on the 'o' before that (pe-RIO-di-co), it needs a written accent mark to break the standard rule.