Learn French: Je ne comprends pas cela. - I do not understand that.

Cela means 'that' in a general, abstract way, like a situation or something someone just said. You use celui-là (that one) or celle-là (that one) only when referring back to a specific masculine or feminine noun that was already mentioned.

Can I use ça instead of cela?

Yes, and in everyday spoken French, you absolutely should! Cela is formal and mostly used in writing. In daily conversation, you will almost always hear Je ne comprends pas ça.

Could I use ce here instead of cela?

No, you cannot say Je ne comprends pas ce. The short word ce is mostly used as a subject with the verb être (to be), as in c'est (it is). As the object receiving the action of a verb like comprendre, you must use the strong form cela or ça.

What verb group does comprends belong to?

Comprends comes from the irregular verb comprendre (to understand). As a helpful shortcut, remember that any verb ending in -prendre is conjugated exactly like prendre (to take): je comprends, tu comprends, il/elle comprend.