There is no single word in English for Iddhi, as the idea is unknown in Europe. The main sense seems to be ʻpotency’.

1. Pre-Buddhistic; the Iddhi of a layman The four Iddhis of a king are personal beauty, long life good health, and popularity (DN.ii.177; MN.iii.176, cp. Ja.iii.454 for a later set). The Iddhi of a rich young noble is 1) The use of a beautiful garden, 2) of soft and pleasant clothing, 3) of different houses for the different seasons 4) of good food, AN.i.145. At MN.i.152 the Iddhi of a hunter is the craft and skill with which he captures game; but at p. 155 other game have an Iddhi of their own by which they outwit the hunter. The Iddhi, the power of a confederation of clans, is referred to at DN.ii.72. It is by the Iddhi they possess that birds are able to fly (Dhp.175).
2. Psychic powers. including most of those claimed for modern mediums (see under Abhiññā). Ten such are given in a stock paragraph. They are the power to project mind-made images of oneself; to become invisible; to pass through solid things, such as a wall; to penetrate solid ground as if it were water; to walk on water; to fly through the air; to touch sun and moon; to ascend into the highest heavens (DN.i.77, DN.i.212; DN.ii.87, DN.ii.213 DN.iii.112, DN.iii.281; SN.ii.121; SN.v.264, SN.v.303; AN.i.170, AN.i.255; AN.iii.17 AN.iii.28, AN.iii.82, AN.iii.425; AN.v.199; Pts.i.111; Pts.ii.207; Vism.378 sq., Vism.384; DN-a.i.122). For other such powers see SN.i.144; iv.290 v.263; AN.iii.340.
3. The Buddhist theory of Iddhi. At DN.i.213 the Buddha is represented as saying: ʻIt is because I see danger in the practice of these mystic wonders that I loathe and abhor and am ashamed thereof’. The mystic wonder that he himself believed in and advocated (p. 214) was the wonder of education. What education was meant in the case of Iddhi, we learn from MN.i.34; AN.iii.425, and from the four bases of Iddhi, the Iddhipādā. They are the making determination in respect of concentration on purpose, on will, on thoughts & on investigation (DN.ii.213; MN.i.103; AN.i.39, AN.i.297; AN.ii.256; AN.iii.82; Pts.i.111; Pts.ii.154, Pts.ii.164, Pts.ii.205; Vb.216). It was ar offence against the regulations of the Sangha for a Bhikkhv to display before the laity these psychic powers beyond the capacity of ordinary men (Vin.ii.112). And falsely to claim the possession of such powers involved expulsion from the Order (Vin.iii.91). The psychic powers of Iddhi were looked upon as inferior (as the Iddhi of an unconverted man seeking his own profit), compared to the higher Iddhi, the Ariyan Iddhi (DN.iii.112; AN.i.93; Vin.ii.183). There is no valid evidence that any one of the ten Iddhis in the above list actually took place. A few instances are given, but all are in texts more than a century later than the recorded wonder. And now for nearly two thousand years we have no further instances Various points on Iddhi discussed at Dial. i.272, 3; Cpd. 60 ff.; Expositor 121. Also at Kv.55; Pts.ii.150; Vism xii; Dhp-a.i.91; Ja.i.47, Ja.i.360.

• -ānubhāva (iddhånu˚) power or majesty of thaumaturgy Vin.31, Vin.209, Vin.240; Vin.DN.iii.iii.67; SN.i.147; SN.iv.290; Pv-a.53
• -ābhisaṅkhāra (iddhåbhi˚) exercise of any of the psychic powers Vin.i.16, Vin.i.17, Vin.i.25; DN.i.106; SN.iii.92; SN.iv.289; SN.v.270 Snp.p.107; Pv-a.57, Pv-a.172 Pv-a.212.
• -pāṭihāriya a wonder of psychic power Vin.i.25, Vin.i.28, Vin.i.180, Vin.i.209; Vin.ii.76, Vin.ii.112, Vin.ii.200; DN.i.211, DN.i.212; DN.iii.3, DN.iii.4, DN.iii.9, DN.iii.12 sq., DN.iii.27; SN.iv.290; AN.i.170 AN.i.292; Pts.ii.227.
• -pāda constituent or basis of psychic power Vin.ii.240; DN.ii.103, DN.ii.115 sq., DN.ii.120; DN.iii.77, DN.iii.102 DN.iii.127, DN.iii.221; MN.ii.11; MN.iii.296; SN.i.116, SN.i.132; SN.iii.96, SN.iii.153 SN.iv.360; SN.v.254, SN.v.255, SN.v.259 sq., SN.v.264 sq., SN.v.269 sq., SN.v.275, SN.v.285; AN.iv.128 sq., AN.iv.203, AN.iv.463; AN.v.175; Mnd.14, Mnd.45 (˚dhīra), Mnd.340 (˚pucchā); Nd i.s. v.; Pts.i.17, Pts.i.21, Pts.i.84; Pts.ii.56, Pts.ii.85 sq., Pts.ii.120 Pts.ii.166, Pts.ii.174; Ud.62; Dhs.358, Dhs.528, Dhs.552; Ne.16, Ne.31, Ne.83; Dhs-a.237; Dhp-a.iii.177; Dhp-a.iv.32.
• -bala the power of working wonders Vv-a.4; Pv-a.171.
• -yāna the carriage (fig.) of psychic faculties Mil.276.
• -vikubbanā the practice of psychic powers Vism.373 sq.
• -vidhā kinds of iddhi DN.i.77, DN.i.212; DN.ii.213; DN.iii.112, DN.iii.281; SN.ii.121; SN.v.264 sq., SN.v.303; AN.i.170 sq., AN.i.255; AN.iii.17, AN.iii.28, AN.iii.82 sq., AN.iii.425 sq.; AN.v.199; Pts.i.111; Pts.ii.207; Vism.384; DN-a.i.222.
• -visaya range or extent of psychic power Vin.iii.67; Ne.23.

Vedic ṛddhi from ardh, to prosper; Pali ijjhati