Learn Spanish (Latin America): Ellos no comprenden el español.

The verb is comprender (to understand), which is a regular -er verb. To say 'they understand', you drop the -er and add the ending for ellos, which is -en.

How come the translation says 'do not', but there is no word for 'do' in the Spanish sentence?

English uses helper words like 'do' or 'does' to make a negative sentence, but Spanish doesn't. You simply put no directly before the verb. So, no comprenden translates perfectly to 'they do not understand'.

Why is there an el before español? We don't say 'the Spanish' in English.

In Spanish, you generally need to use a definite article (like el) before the name of a language. The main exceptions are right after the verb hablar (to speak) or prepositions like en and de. Since the verb here is comprender, we include the el.

Can I leave out the word Ellos?

Yes! Because the verb ending -en already tells us the subject is plural (they or you all), you could just say No comprenden el español. Using Ellos just makes it absolutely clear you mean a masculine or mixed group of 'them'.