Most often, research is done accurately and with integrity. People want to get the job done right. They want to get the answer correct. But sometimes there's something that happens systematically in the experiment or the study that limits the accurate representation of the population that researching.
Bias, in the statistics world, is systematically misrepresenting the population. It refers to the favoring of certain outcomes in a sample that limits our ability to draw conclusions about the population. The key word is systematical--it's not necessarily intentional. It could be intentional, but it doesn't have to be.
A way of selecting the sample for your study such that the sample doesn't accurately reflect the population is called selection bias. It's not good, but sometimes it can't be avoided. On the other hand, sometimes it can be avoided, but isn't.
Publication bias occurs when researchers only want to publish the most sensational findings, or rather, only the positive ones. Only the results that people will want to read make it to people's eyeballs, while findings deemed boring do not.
Often, people will behave differently if they know that they're under observation. They become a bit self-conscious when they are observed and want to do it “right”, so they act differently.
This idea that people might change what they would typically do based on the fact they're under observation is a type of bias called the Hawthorne Effect.
You instruct them not to change their behavior. You don’t want them changing the results by eating differently or exercising more. However, these people might change their behavior based on the fact that they know they're going to be weighed later.
Another thing to consider is when a study is based on participants volunteering their time to be a part of this study. What may happen is that only people with a passion specific to the study may sign up, which is known as participation bias.
Furthermore, another issue may be that the participants tell you what they think you want to hear, which is response bias.
Source: Adapted from Sophia tutorial by Jonathan Osters.