The context and the continuation of the quote from St. Alphonsus de Liguori's book Dignity and Duties of the Priest (Italian: Selva Di Materie Predicabili Ed Istruttive: Per dare gli esercizi a' preti ed anche per uso di lezione privata a proprio profitto.) (1760, republished by the Benzinger Brothers in 1889) explains clearly what "traffic" means: the buying and selling of earthly goods for trading. A Google (literal?) translation of the original Italian is "buying and selling, animal or grain trading, companies, mortgages with interest".
The next paragraph explains the reason: endangering his heart from his main duty. Even when they do business justly, priests also sin against the precept of the Church (is it because of the vow of poverty?). The only exception is when it is strictly necessary by charity.
English translation in the 1889 Benzinger edition
From page 348-349 (within Part II. Material for Instructions, Instruction VIII Mortification, and Particularly Interior Mortification, Section 1. Property which begins at page 345) (emphasis mine):
What a misery to see a priest, who could save souls and do great things for the glory of God, employed in buying and selling, and engaged in traffic of cattle and corn. "You are consecrated," says Peter de Blois, "to great things do not occupy yourself with what is trivial."4 What but a spider's web, says St. Bernard, is earthly traffic? 5 As the spider eviscerates itself, making its web for the purpose of catching a fly, so, O God ! certain priests spend themselves, lose their time, and the fruit of their spiritual works, in order to gain a little dust. They submit to labors, to anxiety and disquietude, for emptiness, when they could possess God, who is the Lord of all things. "Why do we trouble ourselves," exclaims St. Bonaventure, "about nothing, while we may possess the Creator of all things?"
[page 349] Some will say: But I act justly; I attend to this business without any scruple of conscience. I answer, first, that, as has been already said, ecclesiastics are forbidden to engage even in a just traffic: hence if they do not violate justice, they at least sin against the precept of the Church. Besides, St. Bernard says: "Wherever the river flows there it hollows out the earth; so the application to earthly affairs injures the conscience." 1 As in their passage the running waters eat away the banks of the river, so the cares of traffic gnaw the conscience, that is, they make us always fail in some duty. If, says St. Gregory, traffic were productive of no other evil, at least the crowd of worldly thoughts that it engenders closes the ear of the heart, and prevents it from hearing the divine inspirations. 2 In a word, St. Isidore writes: "The more priests occupy themselves with the care of earthly affairs, the more they separate themselves from the things of heaven."3 It is true that some are obliged by charity to attend to the affairs of their family; but, according to St. Gregory, this should be permitted only in cases of strict necessity.4 Some priests undertake, without necessity, the care of the concerns of their family, and even forbid relatives to interfere in them; but if they wished to attend to the affairs of their family why have they become ministers of the family of God ?
Original Italian passage and Google translation
The original Italian of "employed in buying and selling, and engaged in traffic of cattle and corn" is bolded below:
Che miseria è vedere un sacerdote che può salvare anime e fare grandi opere di gloria di Dio, occupato in far compre e vendite, negozj d'animali o di grano, società, mutui con interesse! Magnis addictus es, noli minimis occupari, scrisse Pietro Blessense. Che altro è l'attendere a far negozj di terra, dice s. Bernardo, se non attendere a far tele d'aragni? Fructus illorum quid nisi araneorum telae2? Come il ragno si sviscera per fare la sua tela, affin di prendere poi una mosca; così oh Dio! talun sacerdote si sviscera, perdendo il tempo e il frutto delle sue opere spirituali, e perché? per acquistare un poco di terra. Fatica, s'inquieta per niente, quando può possedere Dio, ch'è il Signore del tutto. Cur nos affligimus, esclama s. Bonaventura, circa nihil, cum possidere creatorem omnium valeamus3?
Google translates the bolded sentence as "busy in buying and selling, animal or grain trading, companies, mortgages with interest":
What misery it is to see a priest who can save souls and do great works for the glory of God, busy in buying and selling, animal or grain trading, companies, mortgages with interest! Magnis addictus es, noli minimis occupari, wrote Pietro Blessense. What else is waiting to do land negotiations, says s. Bernardo, if not wait to make spider webs? Fructus illorum quid nisi araneorum telae2? How the spider eviscerates itself to make its web, in order to then catch a fly; so oh god! some priest eviscerates himself, wasting time and the fruit of his spiritual works, and why? to buy some land. He struggles, he worries about nothing, when he can possess God, who is the Lord of everything. Cur nos affligimus, exclaims s. Bonaventure, circa nihil, cum posdere creatorem omnium valeamus3?