This text is confusingly drafted, in my opinion, because "hold" is used twice in close succession with different objects. "Directors who held office" means "directors who held office as directors", but "those held by their spouses and infant children" means "those interests held by their spouses and infant children". The part that follows the parenthesis clarifies this: it refers to interests in shares, warrants, etc.

Infant children obviously can't hold office as company directors, since directors have to be legally competent. It would be very strange, and probably legally impossible, for an infant child to hold office in a company in any capacity. But that is not what it means. Infant children certainly can have shares registered in their name.

The text refers to Singapore. It occurs verbatim in company reports under the heading "Directors' interests", as in the following example. Note that in the table following this paragraph there is a column headed "Shareholdings registered in the name of director, spouse or infant children". That is what it's about.
http://www.sembcorp.com/en/AR/ar2009/fin_director.htm

Section 150 of the Singapore Companies Act is on appointment of directors. More relevant is section 164, to which the example I have just cited refers ("According to the register kept by the Company for the purposes of Section 164 of the Singapore Companies Act, Chapter 50 (the “Act”)". Subsection 15 of section 164 reads as follows:

"(15) For the purposes of the application of this section —
(a) a director of a company shall be deemed to hold or have an interest or a right in or over any shares or debentures if a wife or husband of the director (not being herself or himself a director thereof) holds or has an interest or a right in or over any shares or debentures or an infant son or infant daughter of that director (not being himself or herself a director) holds or has an interest in shares or debentures; and
(b) any contract, assignment or right of subscription exercised or made by or grant made to the wife or husband of a director of a company (not being herself or himself a director thereof) shall be deemed to have been entered into or exercised or made or, as the case may be, as having been made to the director; and so shall a contract, assignment or right of subscription entered into, exercised or made by or grant made to an infant son or infant daughter of a director of a company (not being himself or herself a director thereof)."
http://statutes.agc.gov.sg/aol/search/display/view.w3p;page=...

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Note added at 5 hrs (2012-10-21 11:48:23 GMT)
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Is it possible for an infant to hold office in a company in Singapore? The phrase in the Companies Act that reads "an infant son or infant daughter of a director of a company (not being himself or herself a director thereof)" (see above) seems to imply that it is. However, that is not relevant here, because "those held by their spouses and infant children" can't refer to offices; it doesn't make sense if you construe it like that. Consider:

"particulars of interests of directors who held office at the end of the financial year (including those offices held by their spouses and infant children) in shares, warrants and share options in the Company".

You can't hold offices in shares, warrants and share options.