I found some articles with the title “Let the Backlash Begin!” and I cannot understand the meaning of the phrase. Could someone explain it?
Backlash, literally, is a reaction against applied force in some mechanism. For example, you adjust the direction a telescope to point in the direction you want, but after you stop the adjustment, it moves back slightly in the direction it came from. More recently, and now more usually it means a reaction - often a strong, negative reaction - against some opinion or policy. In this context we can (for example) talk about street demonstrations being a backlash against government policy.
In the phrase you give - "Let the backlash begin" - there is an invitation to the reader to react against something. There are two possible interpretations, and you will need to judge which applies from the contents of the full article. One is a straightforward call for reaction against someone else's behaviour or views - perhaps a politician or journalist. The other is a more ironic use of the words, where the writer knows they have expressed a controversial opinion and challenges readers to dispute what is written. Allied to this second meaning is the extension where the article supports the controversial views or actions of another person, and again the call for a "backlash" is ironic.