What does it mean when the USCIS states that I might be inadmissible under 212(a)(3)(B) of the INA?

Section 212(a)(3)(B)is a provision of law that was included in the US Patriot Act and provides:

(3) Security and related grounds. -

(B) Terrorist activities-

(i) In general. - Any alien who -

(I) has engaged in a terrorist activity,

(II) a consular officer or the Attorney General knows, or has reasonable ground to believe, is engaged in or is likely to engage after entry in any terrorist activity (as defined in clause (iv),

(III) has, under circumstances indicating an intention to cause death or serious bodily harm, incited terrorist activity,

(IV) is a representative (as defined in clause (v)) of--

(aa) a foreign terrorist organization, as designated by the Secretary of State under section 219, or

(bb) a political, social or other similar group whose public endorsement of acts of terrorist activity the Secretary of State has determined undermines United States efforts to reduce or eliminate terrorist activities,

(V) is a member of a foreign terrorist organization, as designated by the Secretary under section 219, which the alien knows or should have known is a terrorist organization, or

(VI) has used the alien's position of prominence within any country to endorse or espouse terrorist activity, or to persuade others to support terrorist activity or a terrorist organization, in a way that the Secretary of State has determined undermines United States efforts to reduce or eliminate terrorist activities, or

(VII) is the spouse or child of an alien who is inadmissible under this section, if the activity causing the alien to be found inadmissible occurred within the last 5 years, is inadmissible. An alien who is an officer, official, representative, or spokesman of the Palestine Liberation Organization is considered, for purposes of this Act, to be engaged in a terrorist activity.

I don't know the specifics of your case so I can't say why they think that this provision of law applies to you. However, based on the information you provided it appears that they are not denying your case on these grounds. Rather, it appears that they are simply holding your case in order to determine if any of the exemptions apply to your case. The grounds for exemption are:

(ii) Exception. -- Subclause (VII) of clause (i) does not apply to a spouse or child --

(I) who did not know or should not reasonably have known of the activity causing the alien to be found inadmissible under this section; or

(II ) whom the consular officer or Attorney General has reasonable grounds to believe has renounced the activity causing the alien to be found inadmissible under this section.

The law also provides that:

This clause shall not apply to any material support the alien afforded to an organization or individual that has committed terrorist activity, if the Secretary of State, after consultation with the Attorney General, or the Attorney General, after consultation with the Secretary of State, concludes in his sole unreviewable discretion, that this clause should not apply.

So, in your case it appears that they are reviewing whether or not any of the applicable exceptions apply to your case. If you have an attorney I would encourage you to discuss this matter in detail with him or her so they might assist you in obtaining the required exemption.