The Magistrates' Court is the lowest court and is staffed by Magistrates (who are volunteers). Most criminal matters start here before the serious ones are sent up to the Crown Court. Similarly many civil cases start here though some will start in ADR.
A Magistrates' Court will often deal with summary offences. These are small offences with a maximum penalty of 6 months or a fine of £5000. Indictable offences which are more serious will be given a basic trial before being passed to the Crown courts. Either way offences are offences which could be minor or serious depending on the nature of the case itself.
In some cases instead of the magistrates (of which there is generally 3) there will be a District Judge.