It seems to me that 'sent' is a wordplay here that reminds the reader that Jesus is sent by the Father and that the blind man was sent by Jesus. It also seems significant that the water in this pool was used for Sukkot (the Feast of Tabernacles).
Daniel Wallace, in his commentary on the NET translation, notes:
The pool’s name in Hebrew is shiloah from the Hebrew verb “to send.”
In Gen 49:10 the somewhat obscure shiloh was interpreted messianically
by later Jewish tradition, and some have seen a lexical connection
between the two names (although this is somewhat dubious). It is
known, however, that it was from the pool of Siloam that the water
which was poured out at the altar during the feast of Tabernacles was
drawn....
[which is translated “sent”]: This is a parenthetical note by the
author. Why does he comment on the meaning of the name of the pool?
Here, the significance is that the Father sent the Son, and the Son
sent the man born blind. The name of the pool is applicable to the
man, but also to Jesus himself, who was sent from heaven.1
According to InterVarsity Press' Bible Background Commentary on the New Testament,
It is not clear whether “Siloam” meant “sent,” but Greek teachers as
well as Jewish teachers from Philo to the rabbis commonly made
arguments based on wordplays, which were often based on fanciful
etymologies.
Although Siloam was used as a water supply and for baptizing converts
to Judaism, it has more direct significance here. This was probably
still the last day of the Feast of Tabernacles (7:2, 37), and the
water of Siloam was the sacred water used for this feast (see comment
on 7:37–38). Here Jesus employs the ritual water (cf. 2:6; 3:5), but
it works only because the man is “sent.”2
Some early Church fathers made the connection concerning the wordplay as well as linking the event to the sacrament of baptism. For instance, St. Augustine wrote:
He sent him to the pool which is called Siloam. But it was the
evangelist’s concern to call our attention to the name of this pool;
and he adds, “Which is interpreted, Sent.” You understand now who it
is that was sent; for had He not been sent, none of us would have been
set free from iniquity. Accordingly he washed his eyes in that pool
which is interpreted, Sent—he was baptized in Christ. If, therefore,
when He baptized him in a manner in Himself, He then enlightened him;
when He anointed Him, perhaps He made him a catechumen. In many
different ways indeed may the profound meaning of such a sacramental
act be set forth and handled; but let this suffice your Charity. You
have heard a great mystery.3
Concerning the word 'sent' itself, the Greek word (ἀπεσταλμένος) literally means "sent out/away."4 The Hebrew word being referenced by the Greek word may refer to a "flowing out (of waters)." According to Vincent,
The Hebrew word means outflow (of waters); missio, probably with
reference to the fact that the temple-mount sends forth its
spring-waters. Many expositors find a typical significance in the fact
of Christ’s working through the pool of this name. Thus Milligan and
Moulton, after noting the fact that the water was drawn from this pool
for pouring upon the altar during the Feast of Tabernacles; that it
was associated with the “wells of salvation” (Isa. 12:3); and that the
pouring out of the water symbolized the effusion of spiritual blessing
in the days of the Messiah, go on to say: “With the most natural
interest, therefore, the Evangelist observes that its very name
corresponds to the Messiah; and by pointing out this fact indicates to
us what was the object of Jesus in sending the man to these waters. In
this, even more distinctly than in the other particulars that we have
noted, Jesus, in sending the man away from Him, is keeping Himself
before him in everything connected with his cure. Thus, throughout the
whole narrative, all attention is concentrated on Jesus Himself, who
is the Light of the world, who was ‘sent of God’ to open blind
eyes.”5
It should be noted that this definition is somewhat disputed. The word in Hebrew may also only mean "sending away."6
Ultimately, the wordplay seems to be the best explanation.
Sources
1 Biblical Studies Press, The NET Bible First Edition Notes (Biblical Studies Press, 2006), Jn 9:7.
2 Craig S. Keener, The IVP Bible Background Commentary: New Testament (Downers Grove, IL: InterVarsity Press, 1993), Jn 9:7.
3 Augustine of Hippo, "Lectures or Tractates on the Gospel According to St. John", trans. John Gibb and James Innes, in A Select Library of the Nicene and Post-Nicene Fathers of the Christian Church, First Series, Volume VII: St. Augustin: Homilies on the Gospel of John, Homilies on the First Epistle of John, Soliloquies, ed. Philip Schaff (New York: Christian Literature Company, 1888), 245.
4 William Arndt, Frederick W. Danker and Walter Bauer, A Greek-English Lexicon of the New Testament and Other Early Christian Literature, 3rd ed. (Chicago: University of Chicago Press, 2000), 120.
5 Marvin Richardson Vincent, Word Studies in the New Testament (New York: Charles Scribner’s Sons, 1887), Jn 9:7.
6 Francis Brown, Samuel Rolles Driver and Charles Augustus Briggs, Enhanced Brown-Driver-Briggs Hebrew and English Lexicon, electronic ed. (Oak Harbor, WA: Logos Research Systems, 2000), 1019.
