Basically, if evidence is to be admitted at court, it must be relevant, material, and competent. To be considered relevant, it must have some reasonable tendency to help prove or disprove some fact. It need not make the fact certain, but at least it must tend to increase or decrease the likelihood of some fact.
Once admitted as relevant evidence, the finder of fact (judge or jury) will determine the appropriate weight to give a particular piece of evidence. A given piece of evidence is considered material if it is offered to prove a fact that is in dispute in a case. Evidence is considered "competent" if it complies with certain traditional notions of reliability. Courts are gradually diminishing the competency rules of evidence by making them issues related to the weight of evidence.
There are different types of evidence that may be available in a criminal case. The four basic forms of evidence are:
Some rules of evidence apply to all four types and some rules apply to one or two of them. All of these forms of evidence must be admissible, though, before they can be considered as probative of an issue in a trial.
Testimonial evidence is where a person takes the stand and answers questions about a case. However, because people's statements can be tainted by poor memories or bias, a number of admissibility rules apply.
For example, while witnesses may testify as to what they observed or perceived during an event, in some situations they may also testify about statements they heard outside of court (that weren't made under oath). Such statements often constitute hearsay evidence and are generally not admissible because they're not as reliable as statements made in court and under oath. However, there are many exceptions to the hearsay rule allowing for the admission of statements made outside of court.
There are also times when a witness may seek to provide testimony about a person's character, often to make the point that the person is the "type" of person who would or wouldn't say or do what is at issue in a case. Like hearsay evidence, this type of evidence also has reliability problems as it does not directly show whether the person actually did or said something. Because of this, character evidence is generally not admissible, but there are exceptions.
Finally, there are times when certain evidence is so complicated, like DNA evidence, that it requires an expert to interpret and explain it to the court. This type of expert testimony is only admissible once the expertise of the witness is established and their testimony is found to be based on reliable methods and acknowledged within the scientific community.
When one side of a case tries to introduce evidence that isn't relevant, material or competent, the other side can ask, before or during trial, to have the evidence suppressed on admissibility grounds. One area where a motion to suppress is commonly raised is with chain of custody issues where a piece of evidence isn't properly secured from its collection to trial.
So, for example, if one side can show that a blood sample was not properly labeled or a weapon wasn't properly locked in an evidence room, there's no way to trust the results of any subsequent blood test or a fingerprint analysis. While this evidence may be relevant and material, it would not be competent because of intervening custody problems that could have led to inaccurate test results.
A strong criminal defense attorney will not only challenge the prosecutor's evidence, but also help to discover and present stronger evidence in your favor. Because of this, it's important to give your attorney as much time as possible on your case. If you're charged with a crime, don't delay; find an experienced criminal defense lawyer near you.