The protections enshrined in the ubiquitous words of the Miranda rights are meant to protect your right against self-incrimination. However, these rights are not self-executing, and require affirmative invocation in order to be effective. The need for invocation is particularly important regarding the right to remain silent.
In order to invoke your right to silence, you must affirmatively invoke that right. Following the decision of Berghuis v. Thompkins The Supreme Court in a 5-4 judgment has held that to invoke your right to remain silent, you must affirmatively invoke that right. If you fail to affirmatively invoke your right to silence but remain silent, that silence may be used against you to show that you had knowledge of your right to remain silent.