Short answers, pulled from the story.
Yogachara is a Sanskrit compound that literally means "practice of yoga" or "one whose practice is yoga," making the school's name literally "the school of the yogins." It was also known by other names including Vijnanavada, meaning the doctrine of consciousness, and Vijaptimatra-vada, meaning the doctrine of mere representation.
The brothers Asanga and Vasubandhu, both active around the fourth to fifth century, are considered the classical philosophers and systematizers of Yogachara. Buddhist tradition also attributes the school's founding inspiration to the figure Maitreya-natha. Later, Xuanzang brought the tradition to China in the seventh century and Shantaraksita brought it to Tibet in the eighth century.
Vijnapti-matra, usually translated as "consciousness-only" or "mind-only," is the central Yogachara claim that we are only ever aware of mental images or impressions which manifest as external objects, while there is no such thing outside the mind. The earliest surviving use of the term appears in chapter 8 of the Sandhinirmocana Sutra, where the Buddha says the images in meditative concentration are not separate from the contemplating mind because they are vijnapti-matra.
Yogachara expanded the standard Buddhist model of six consciousnesses by adding two more: the seventh is the defiled self-consciousness, which constantly mistakes the eighth consciousness for a genuine self; the eighth is the alaya-vijñana or storehouse consciousness, which holds all karmic seeds until they ripen into experience. The five sense consciousnesses, the integrating mental consciousness, and these two additional ones together form the eight bodies of consciousnesses.
The Chinese pilgrim Yijing, who lived from 635 to 713, summarized the core difference: Yogachara holds that the real exists but the conventional does not, while Madhyamaka holds that the real does not exist but the conventional does. Yogachara affirmed that the dependent nature, the stream of conscious transformation, really exists and that emptiness is a genuine absence, while Madhyamaka refused to endorse such existential assertions about anything.
This is actively debated. Scholars including Lambert Schmithausen, Jay Garfield, and Paul Williams affirm an idealist reading, noting that Yogachara texts clearly reject mind-independent external objects. Other scholars including Anacker and Lusthaus argue it is better understood as a soteriological phenomenology: a therapeutic and epistemic project aimed at understanding how the mind constructs experience, rather than a metaphysical claim that only minds exist.