A taqsim is a melodic musical improvisation. In Middle Eastern classical belly dance music a taqsim is usually done by a violin, accordion, oud or kanoun. They can range in length from short to really long and can often flow from one instrument to the next. When dancing to a taqsim the dancer should portray a different mood or feeling to each instrument doing the taqsim. There is also a more intimate, internal moment portrayed by the dancer giving less energy to the audience as she would when the whole orchestra is playing together.
A beledi section is most commonly started with an accordion taqsim then the drum is added in.
Pictured below is a kanoun and an oud, two of my favorite interments to do taqsims to. The kanoun has 72 stings and if played laying down. Shimmies are usually done when dancing to a kanoun. The oud is danced to with abdominal movements.
Here is a video of Talia dancing to a live violin taqsim: