The first house is the first of the twelve houses, the divisions of the horoscope that describe the fields of life through which the planets act. It begins at the ascendant, the point of the zodiac rising on the eastern horizon at the moment in question, and it is the most personal of the houses, governing the self, the body, the physical appearance, and the temperament, the way a person meets and enters the world. It is an angular house, one of the four strongest, cadenced by the horizon and meridian; planets placed in the angular houses are held to act with the most force. These are the interpretive conventions of the astrological tradition for this division of the chart, in which the first house sets the tone of the whole nativity as the lens through which everything else is expressed.
The twelve-house system itself is a Hellenistic development, already assumed as traditional by Vettius Valens writing around 175 CE and set out systematically two centuries later by Paulus Alexandrinus in 378. Greek astrologers called the first house the Horoskopos, the hour-marker, the very point that names the whole art of casting a horoscope, and held that Mercury has his joy here, one of seven places across the wheel where a particular planet was said to delight and act with special ease, a doctrine older than and separate from the dignities of rulership and exaltation. That the ascendant should be Mercury's joy fits the house's character in the later tradition as well, the point of quickest, most immediate self-expression, the mind's first contact with the world before any other planet has had its say.
Sources A History of Western AstrologyNicholas Campion with Introduction to Astrology (Eisagogika)Paulus Alexandrinus