whenever there is a "degree of uncertainty" it means that there is something unknown, so you can't predict the outcome. In other words there are some variables that may influence the outcome and you might have an expectation what is going to happen, but you are also aware that there is a high probability that something else happens.

"Degree" can mean "a way of measuring the amount of something," as in "degrees Centigrade." A "college degree" measures how advanced your education is. "There is a degree of uncertainty" literally means "there is some amount of uncertainty." It is a way of being vague. "There is a degree of uncertainty" is in between "It is certain" and "It is highly uncertain." It means it might be fairly certain, but, nevertheless, there is some uncertainty. "How long does it take to drive from New York to Boston?" "About four hours, but there is a degree of uncertainty because of traffic and road construction."