The Fourth Amendment to the U.S. Constitution protects its citizens from unlawful searches and seizures from the government. You have a reasonable expectation of privacy in many places and things, and the government cannot search or seize them without either reasonable suspicion and/or probable cause.
If the government has obtained evidence against you in an illegal manner, then your attorney will file a motion to suppress this evidence. At this hearing, your attorney will argue that the government (e.g. the police) did not have lawful grounds to search a specific place or seize particular things. If you prevail in the motion to suppress hearing, then the government will be prohibited from using any illegally obtained evidence against you. Often times, this means the government cannot successfully meet all the elements of the crime you have been charged with. For example, if you were arrested and charged with possession of marijuana, but, after a motion to suppress, the judge finds the police violated your Fourth Amendment right while confiscating it, then the government will not be able to use the marijuana in their case against you. Without meeting this essential element of the crime, the government cannot prove its case.
By no means is a motion to suppress a simple issue. Often times, your attorney will have to develop sound arguments both in fact and in law in order to build a good motion. Thus, it is important you hire an attorney who has the necessary skills and experience.