Moe is used to describe extremely idealized characterizations, whether it's their looks or certain personality traits. It's usually applied to younger, female characters in anime. The character does not need to be "perfect," per se, but there are traits within that character that hold a certain attraction to viewers. An example of a moe character would be
Hirasawa Yui from
K-ON!
In this case, moe can also refer to the style to which anime has turned in the past few years. They bear a huge similarity to the artstyle of K-ON!'s anime series, and feature girls for the most part. I mention K-ON! because it is the simplest to refer to, but that does not exclude other anime from being defined as 'moe.' It features looser animation and more emphasis on facial expressions and endearing the character as much as possible through the animation. The trend can be compared to the
shoujo manga style that was prominent until the 90s (I believe? The example given is one from the 70s.)