I know that exciton is an electron and hole orbiting around each other(at least that is what I have heard). So if the hole is a hypothetical particle with a plus sign, meaning that it is a lack of an electron jumping around in a certain material, how should I imagine hole jumping out to the gap in a semiconductor and there orbiting around with an electron. Is that the one-electron-less atom that does it or is that just made out idea like a hole?
An exciton really is a electron coupled to a hole, just as you said. A electron gets excited to a higher band, leaving a hole in the lower band behind (a bit like a bubble on top of a liquid). You can disregard the other electrons (and holes) in this picture, as they are smeared out and just form the background.
The electron and the hole are attracted to each other, and form a pair, just like a Hydrogen atom (electron+proton) or positronium (electron+positron). Since electrons are lighter than protons, the radius of the exciton is much larger than that of a Hydrogen atom. Actually, what counts are the effective masses of electron and hole.
Since you are talking about semiconductors, you are probably concerned with Wannier-Mott excitons. These have an especially large radius, larger than the lattice constant, since a screening effect reduces the coulomb attraction between electron and hole further.
Eventually, electron and hole will recombine, but it can take a while compared to other time scales. One reason is that the lattice has to carry away the exact excess energy and momentum of the exciton (its QM). Also, the wavefunctions of electron and hole don't overlap very much, further reducing the probability of recombination.
For further info, the Wikipedia article on Excitons seems not too bad.