First, do not ever -- EVER -- blow off jury duty. They can issue a bench warrant for your arrest. And yes, I have seen that happen before.
Secondly, what you describe being called for the 20th and the 21st, I agree with the "on call" answerer. I've been called numerous times and have had my jury duty canceled for the same reasons: Case settled.
Thirdly, how jury duty actually works is pretty simple. The county in which you live randomly sends out jury summons based on voter and tax rolls. The person receiving the summons shows up for jury duty and is given a jury questionnaire to fill out that provides basic information.
Those jury questionnaires are then given to the judge and both sets of attorneys, plaintiff and defense, to enable them to know something about you and to ask you questions about later on if you actually make it into a courtroom. This process is called voir dire. It's a long, drawn-out process to find suitable jurors to hear a case. They will tell you up front of it is civil or criminal.
Once you get called into the courtroom, the judge will ask you if you know any of the parties in the case, any of the attorneys, and any of the witnesses. The attorneys will then, with your form in hand, ask you all kinds of questions about your biases or lack thereof. For instance, one question you might get is if you've ever been the victim of a crime. This is especially important in criminal cases because, God forbid, it's a bank robbery, as an example, and last year you were held up in a bank. You're probably not going to do well on that jury. At that point, the judge could send you back to the jury room, or he/she could dismiss you altogether.
If you get chosen as a juror, you will be sworn under oath to listen to the evidence and examine the exhibits, and to come to a true and just verdict. You will then be presented with evidence, witness testimony, exhibits, and when the case is done, the judge will instruct you on the law and you will retire to the jury room to deliberate with your fellow jurors. You will all discuss with each other all of the evidence, etc., until you all reach a conclusion.
Jury duty is your civic duty, and justice cannot be done for anyone without a jury. It is not only your Constitutional right, it is also your Constitutional duty. Most times, for most of us, it's a day out of our lives. It is a very interesting process, and jurors do a wonderful job of really listening to the evidence and, most times come to just verdicts. It can't happen without you.