What is "state of perfection"? What does Aquinas mean when he speaks of "state of perfection", or more broadly, what does Catholic Church mean by "state of perfection"? He often uses this phrase in works like Summa Theologiae, On the perfection of spiritual life etc.
Referring to St. Thomas Aquinas's De perfectione vitæ spiritualis c. 15, Fr. Royo Marín, O.P., in La vida religiosa p. 116, defines "state of perfection" in general:


  States of Christian perfection are those whose members are obliged in a permanent and stable manner, through certain means,* to acquire Christian perfection or to exercise it for the good of others.
  
  [Son aquellos estados de vida cristiana cuyos miembros se obligan de una manera permanente y estable, mediante determinados medios, a adquirir la perfección cristiana o a ejercitarla en bien de los demás.]


*such as a rule approved by the Church, like St. Benedict's Rule or St. Augustine's Rule

Thus, "state of perfection" can be divided into that for


acquiring perfection


Religious life, whose primary object is God.cf. Summa Theologica II-II q. 186 a. 1 "Whether religion implies a state of perfection?"

exercising perfection for the good of others


Episcopal state, whose object is the good of others out of the love of God.



St. Thomas's articles on the question of the state of perfection in general (Summa Theologica II-II q. 184) are well worth reading. Relevant here are articles


1. Whether the perfection of the Christian life consists chiefly in charity?A thing is said to be perfect in so far as it attains its proper end, which is the ultimate perfection thereof. Now it is charity that unites us to God, Who is the last end of the human mind, since "he that abideth in charity abideth in God, and God in him" (1 Jn. 4:16). Therefore the perfection of the Christian life consists radically in charity.
4. Whether whoever is perfect is in the state of perfection?properly speaking, one is said to be in the state of perfection, not through having the act of perfect love, but through binding himself in perpetuity and with a certain solemnity to those things that pertain to perfection.cf. II-II q. 186 a. 1 ad 3: "it does not follow that whoever is in the state of perfection is already perfect, but that he tends to perfection." Even those who struggle upholding the 10 Commandments are permitted to enter religion, because "the religious state is a spiritual schooling for the attainment of the perfection of charity," "accomplished through the removal of the obstacles to perfect charity by religious observances" (II-II q. 189 a. 1 co.).
7. Whether the religious state is more perfect than that of prelates [bishops]?As Augustine says (Gen. ad lit. xii, 16), "the agent is ever more excellent than the patient." Now in the genus of perfection according to Dionysius (Eccl. Hier. v, vi), bishops are in the position of "perfecters," whereas religious are in the position of being "perfected"; the former of which pertains to action, and the latter to passion. Whence it is evident that the state of perfection is more excellent in bishops than in religious.It is from the abundance of their love of God that bishops are able to love their flock. This is why Jesus first asked St. Peter if he loved him and then commanded him to feed His flock (John 21:15-17).


cf. Fr. Hardon, S.J.'s definition of "state of perfection" as


  Those stable forms of living in which some of the faithful bind themselves by vows, or promises equivalent to vows, to practice the evangelical counsels of poverty, chastity, and obedience. They are called states of perfection because those who live in these states agree to follow a particular rule of life, approved by the Church, whose faithful observance will certainly lead to Christian perfection.