A technicality is a trivial or very small detail. You might consider your scuffed, unpolished shoes to be an unimportant technicality when you're dressing for a job interview.
You can use the noun technicality for any small point or detail, but it's most likely to come up in the context of a court trial or a conversation with an attorney. A legal technicality is a small but ultimately important detail of the law. For example, a robbery suspect might have his trial dismissed on a legal technicality if the arresting police officer neglected to show him a search warrant before searching his house.