What is a mathematical trapdoor and how is it used with encryption?

What will be an ideal response?

A mathematical trapdoor is a "secret mechanism that enables you to easily accomplish the reverse function in a one-way function." With a trap-door, you can use a key to encrypt or decrypt the ciphertext, but not both, thus it requires two keys. The public key becomes the true key, and the private key is derived from the public key using the trapdoor.