This, of course, refers to Dependent Origination, with upadhi used synonymously with upādāna.
Pali Text Society's dictionary equates it with taṇhā:
Upadhi, (fr. upa + dhā, cp. upadahati & BSk. upadhi Divy 50, 224, 534) 1. putting down or under, foundation, basis, ground, substratum (of rebirth) S. I, 117, 124, 134, 186; A. II, 24 (°saṅkhaya); III, 382 (id.); IV, 150 (°kkhaya); It. 21, 69; Sn. 364, 728 (upadhī-nidānā dukkha = vaṭṭa-dukkhaṃ SnA 505), 789, 992; Nd1 27, 141; Nd2 157; Vbh. 338; Nett 29; DhA. IV, 33.—(2) clinging to rebirth (as impeding spiritual progress), attachment (almost syn. with kilesa or taṇhā, cp. nirupadhi & anupadhi); S A. = pañcakkhandhā, S. II, 108. At M I 162 (cp. Sn. 33 = S. I, 6 = I. 107) wife and children, flocks and herds, silver and gold are called upadhayo. upadhi is the root of sorrow ib. 454; S. II, 108; Sn. 728 = 1051 = Th. I, 152 and the rejection of all upadhis is Nibbāna D. II, 36. (cp. S. I, 136; III, 133; V, 226; A. I, 80; M. I, 107 = II. 93; Vin. I, 5, 36 = J. I, 83 = Mvst II. 444; It. 46, 62); D. III, 112 calls that which has upadhi ignoble (= non-Aryan). At S. I, 117 = Divy 224 upadhi is called a bond (saṃgo). Cp. opadhika.—The upadhis were later systematized into a set of 10, which are given at Nd2 157 as follows: 5 taṇh’upadhis (taṇhā, diṭṭhi, kilesa, kamma, duccarita), āhār-upadhi, paṭigh°, catasso upādinnā dhātuyo u. (viz. kāma, diṭṭhi, sīlabbata, attavāda; see D. III, 230), cha ajjhattikāni āyatanāni u. , cha viññāṇa-kāyā u. Another modified classification see at Brethren p. 398. (Page 142)
In my understanding, the idea here is that the pursuit of acquisitions has a semiotic effect of cementing the notion of self as an agent of action and enjoyer of its results. And so craving for an object, setting one's mind onto the object, making the object one's target, pursuing the object, acquiring the object, and then enjoying the contact with the object is exactly the semiotic sequence that leads to bhava - becoming (=identifying self as) a sentient being.
While experience of "contact" with an "object" marks the point when the spatial sense of self has fully matured, it is pursuit and acquisition is what helps the temporal sense of self to come to fruition.
Once self-identification as sentient being has fully matured both spatially and temporally, the self imputed onto the aggregates becomes subject to change of the aggregates, hence "aging-and-death".