A motion to suppress is a request that evidence not be presented at trial because an attorney has reason to believe that the evidence was unlawfully obtained or that it cannot be legally presented due to restrictions in the law. Motions to suppress are generally filed as part of the pretrial motions. A judge determines whether or not to grant the motion, depending on the supporting materials presented, either admitting the evidence or agreeing that it should be excluded.
Attorneys may file motions to suppress for as much evidence as possible, even if they think it's probable that the evidence will be admitted anyway. It may be worth taking a chance to get particularly problematic evidence excluded, and the motions will remain on the record even if the evidence is admitted, which can be useful when filing an appeal or challenging the outcome of a trial. In this case, the lawyer may argue that the motion to suppress was unreasonably denied and that the evidence tainted the outcome of the trial.
One common reason to file a motion to suppress is the belief that the evidence was unlawfully obtained. Many nations have specific rules about how evidence can be collected, when law enforcement can make traffic stops, and so forth. If these rules are violated, the evidence obtained may not be allowable. For example, in the United States there are protections against search and seizure which can be used to try and strike evidence obtained in ways which are not legal.
If a lawyer believes that the actions used to collect evidence cannot be justified under the law, a motion to suppress can be filed. This is one reason why law enforcement officers are very careful about documenting every action they take and why so that their actions will hold up in court and the evidence they collect will be admitted. Documentation often includes video recordings of interactions with the public so that there can be no dispute about what happened and when during interviews, traffic stops, and other interactions.
The motion to suppress is a formal written document which discusses the evidence in question and the reasons that the lawyer is requesting exclusion. Typically both sides in a case present motions before the start of trial. The judge may potentially ask the lawyers for a meeting to discuss particular motions which seem to require more clarification or consultation. Pretrial motions from the defense may also include a request to dismiss the trial altogether, although these motions are rarely granted.