A rehearsal is a practice before a concert or play in a theatre or some other performance. The group of performers will get together to rehearse. They may rehearse together many times before the performance so that they get used to performing with one another.
A dress rehearsal is the last rehearsal before the performance. It is called a 'dress rehearsal' because in a theatre the actors will be wearing their costumes. When an orchestra or other music group have a 'dress rehearsal' this does not mean that they have to dress up. It simply means that it is the last rehearsal, and it will be in the hall where they are going to perform so that everything is as it will be for the performance.
Orchestras often have section rehearsals or sectionals. This means that each group of instruments rehearse separately, e.g. the string sectional will be all the string instruments rehearsing together. This can be useful because they can concentrate on the bits which are particularly difficult for them: the string instruments can talk about the bowing etc.
An open rehearsal is a rehearsal that the public can come and watch. In opera houses the dress rehearsal is often an open rehearsal. The entry may be free or the audience may have to pay, but not as much as for a ticket for a performance. The audience will have to understand that the performance may be stopped if something goes wrong and needs to be rehearsed. Singers will often save their voices by not singing as loudly as they will in the performance (this is called "marking").
Rehearsal Facts for Kids. Kiddle Encyclopedia.