The phrase doesn't appear very much. The NIDNTTE, which usually has sizable paragraphs of description, has the following. But the listing does give us a decent synopsis of how the phrase is used:
JL 1 In the LXX the vb. καταβάλλω occurs c. 45x (incl. 11x in
Ezekiel) to render a variety of Heb. terms, esp. the hiph. of נָפַל
H5877 (“to cause to fall down,” thus also “to tear down, destroy,”
etc.; e.g., of breaking down a city wall, 2 Sam 20:15). Only in 2 Macc
2:13 does it have the sense “to found” (Nehemiah founded a library by
collecting the ancient writings of Israel; cf. also 5:6, of setting up
monuments). No theological significance attaches to the use of this
term. The noun καταβολή occurs but once, with ref. to the
construction of a house (2:29).
2 It is worth noting that the Letter of Aristeas uses καταβολή
twice: once with ref. to the foundation of the temple (§89) and once
in the phrase μία καταβολή with ref. to the “one creation” (§129);
it also uses καταβάλλω with the noun διδαχή G1439 to describe the
laying of foundational teaching (§294). The vb. is found with some
freq. in both Philo and Jos. (the former uses it several times with
the sense “to sow, implant,” both lit. and fig., e.g., of sowing
plants (i.e., virtues or vices) in the soul, Leg. 1.49). The noun
occurs occasionally, as when Jos. speaks of ἀποστάσεως καταβολή,
“the beginning of a revolt” (B.J. 2.260), or when Philo uses the
phrase ἡ πρώτης καταβολὴ τῆς τούτων γενέσεως, “the first origin
of the birth of these [i.e., the Hebrews]” (Mos. 1.279).
NT 1 The vb. καταβάλλω occurs 2x in the NT: once in the lit. sense
“to strike down” (2 Cor 4:9), and once of laying the foundation
(θεμέλιον καταβαλλόμενοι) of Christian doctrine (Heb 6:1, parallel
with ὁ τῆς ἀρχῆς τοῦ Χριστοῦ λόγον, lit., “the teaching of the
beginning of Christ,” i.e., the basic teaching about Christ). The noun
occurs 11x, once in the expression καταβολὴ σπέρματος (Heb 11:11),
which would normally refer to the man’s part in procreation,
“begetting” (cf. NRSV, NIV 1984), but here the subj. is apparently
Sarah, so the meaning may be more general, “having children” (cf. NIV
2011; see also Σάρρα G4925). All of the remaining instances consist
of the combination ἀπὸ [or πρὸ] καταβολῆς κόσμου, “from [or
before] the foundation of the world” (with the poss. exception of Matt
13:35, where the word κόσμου is textually suspect, but the meaning is
the same). The rest of the art. is devoted to this phrase.
2 It is clear that καταβολὴ κόσμου has become a fixed expression
for the point from which historical dates are reckoned (cf. the use of
A.M., Anno mundi, in Jewish chronology). When God’s free activity is
dated before (πρό) this point in time, as in John 17:24 (where the
obj. of God’s love is Jesus) and Eph 1:4 (where the obj. is the
believer), the purpose is to declare the independence of God’s
providence from the abs. beginning that he himself set and thus from
history. This independence enables him to break into history in his
loving purposes and to bring the course of history to its completion,
again in his love. Two points stand out in all the texts that mention
the foundation of the world. First, it is always associated with a
statement about human destiny. Second, there is an implied connection
between God’s foreknowledge and predestination. In partic., Matt 25:34
and Eph 1:4 speak of election (see ἐκλέγομαι G1721). In the case of
Rev 13:8 and 17:8, the theme is reprobation. Luke 11:50 (a lamentation
of Jesus) and Heb 4:3 speak of historical failure for which account
must be rendered. Finally, the unique, central position of Jesus
Christ in the history of salvation is highlighted in Matt 13:35
(quoting Ps 78:2 [LXX 77:2], with some textual differences, such as
καταβολή where LXX has ἀρχή); Heb 9:26; and 1 Pet 1:20 (cf. John
17:24). He reveals in the midst of history what has been hidden since
the foundation of the world, and thus fixes the end of time. The
phrase “before the foundation of the world” (John 17:24; Eph 1:4; 1
Pet 1:20) is foreign to the OT and is prob. an attempt to express the
independence of the Creator from his creation in the face of
Hellenism—and thus to make his acts of salvation dependent on him
alone.
(The New International Dictionary of New Testament Theology and
Exegesis, s.v. “καταβολή καταβάλλω,” 2:635-636.)