Cherry picking is when someone picks the case which supports his opinion.
For example, suppose twenty studies have been done on a new medicine and 19 say it works, but one says it does not work. To "cherry pick" is to use the one failed study to "prove" that the medicine is useless. It is a type of confirmation bias, where a person sees evidence for what they want or expect to see, and ignores evidence which goes against their belief.
The term cherry picking comes from when people harvest cherries from a tree - the cherry picker only takes the reddest, ripest fruits. If someone looked at all the fruit the person had picked, they might think that all the cherries were red, until they went to the tree and saw lots of pale, unripe cherries still on it.
Cherry picking as a term is quite negative, as it implies that the person doing the cherry picking is trying to deceive the audience, or simply does not care about the facts.
Cherry picking can take several forms. The most obvious case of cherry picking is where only evidence that supports a given argument is used, and other evidence which does not support it or goes against it is ignored or covered up. Other examples can include giving a lot of emphasis to evidence which supports the idea but barely any to other evidence, and taking a quote out of context so that it seems to have a different meaning than it originally did.
Pseudoscience is when untrue claims are made to appear as though they have a scientific basis, even though they do not. Many pseudoscientists cherry pick real scientific evidence to support their claims. It is quite common in science for some studies to contradict others, for example in cases where different methods are used to measure an outcome, or where human error or chance may lead to unusual results. This means that there is often a study someone can use to support their claim, and they can cherry pick that one study even if many more contradict it.