Taurus, Leo, Scorpio and Aquarius are the signs the Sun occupies in the middle month of each season. Ptolemy calls them the solid signs, stereos, and the reason he gives is meteorological: while the Sun passes through them, the character of the season is settled and fully itself rather than arriving or departing.
That is the whole of the doctrine and everything else follows from it. The tradition reads the fixed signs for holding a position, resisting change and seeing a thing through, and for the difficulty of moving anything that has settled into them. Their reputation for stubbornness is a fair reading of the same property from the other side.
The group has an unusual afterlife outside astrology. The four are represented by a bull, a lion, an eagle and a man, and that set of figures appears in the vision of Ezekiel, in the four living creatures of the book of Revelation, in the four evangelists of Christian iconography, and on the World and the Wheel of Fortune in the tarot. Whether the correspondence runs from astrology into the religious imagery, in the other direction, or from a shared older source, is a question with real scholarship on more than one side, and this entry does not settle it.
The eagle for Scorpio is itself a substitution. The sign's own creature is the scorpion, and the eagle appears as its higher form within a tradition of interpretation rather than in the sign's basic definition.