The isolated example or anecdotal fallacy is utilizing "a personal experience or an isolated example instead of a sound argument or compelling evidence." This fallacy appeals to one or two examples as proof that whatever is being claimed is generally true.
1) Obamacare is a disaster. My sister's health insurance has tripled with far less coverage.
It is, of course, true that under the Affordable Care Act, there are people that have found their health insurance less affordable, but evidence here or there doesn't tell us what the overall picture is on the ACA's affordability.
2) Obamacare is great for America! For the first time in my working life, I have health insurance.
It is also true that with the ACA there are those who have health insurance who did not have it before, but again, an appeal to one example does not give us the larger perspective.
Let me use two non-political examples to clarify. The first one is provided by yourlogicalfallacyis.com:
1) My grandfather smoked until he was 97 and never got cancer or any other bad stuff. I don't believe all the hype about the hazards of smoking.
Many studies over the years have made the clear connection between smoking and various health problems. Just because one guy lived to be almost a centenarian and smoked like a chimney does not cast doubt upon the evidence.
2) I got a flu shot once and got sick anyway. Flu vaccines are worthless.
Again, the evidence has been clear since the introduction of vaccinations-- vaccines guard against all kinds of illness. The fact that one person got the flu in spite of the vaccine means nothing in the larger context.
There is nothing wrong with appealing to personal experience as that experience specifically affects that individual, but to use anecdotal evidence to make general and sweeping claims is bad logic.
The next logical fallacy: cherry-picking