Executive sessions can be called by a MAJORITY vote to discuss the following topics:

* dismissal, promotion or compensation of public employees including investigations and disciplinary hearings assuming that the individual in question has not requested an open meeting
* hiring discussions
* matters that would adversely affect the reputation of an individual
* sale or purchase of property
* information that would fall under attorney-client privilege exemptions concerning pending litigation
* applications for the adult parole board
* security information
* to protect trade secrets of applicants[1]

Decisions made during executive session require a 2/3 vote and must be made public within 72 hours of the close of the meeting.[1] 

http://ballotpedia.org/New_Hampshire_Open_Meetings_Law

RSA 91-A:3 Nonpublic Sessions. –  
I. (a) Public bodies shall not meet in nonpublic session, except for one of the purposes set out in paragraph II. No session at which evidence, information, or testimony in any form is received shall be closed to the public, except as provided in paragraph II. No public body may enter nonpublic session, except pursuant to a motion properly made and seconded. 
(b) Any motion to enter nonpublic session shall state on its face the specific exemption under paragraph II which is relied upon as foundation for the nonpublic session. The vote on any such motion shall be by roll call, and shall require the affirmative vote of the majority of members present. 
(c) All discussions held and decisions made during nonpublic session shall be confined to the matters set out in the motion. 
II. Only the following matters shall be considered or acted upon in nonpublic session: 
(a) The dismissal, promotion, or compensation of any public employee or the disciplining of such employee, or the investigation of any charges against him or her, unless the employee affected (1) has a right to a meeting and (2) requests that the meeting be open, in which case the request shall be granted. 
(b) The hiring of any person as a public employee. 
(c) Matters which, if discussed in public, would likely affect adversely the reputation of any person, other than a member of the public body itself, unless such person requests an open meeting. This exemption shall extend to any application for assistance or tax abatement or waiver of a fee, fine, or other levy, if based on inability to pay or poverty of the applicant. 
(d) Consideration of the acquisition, sale, or lease of real or personal property which, if discussed in public, would likely benefit a party or parties whose interests are adverse to those of the general community. 
(e) Consideration or negotiation of pending claims or litigation which has been threatened in writing or filed against the public body or any subdivision thereof, or against any member thereof because of his or her membership in such public body, until the claim or litigation has been fully adjudicated or otherwise settled. Any application filed for tax abatement, pursuant to law, with any body or board shall not constitute a threatened or filed litigation against any public body for the purposes of this subparagraph. 
(f) Consideration of applications by the adult parole board under RSA 651-A. 
(g) Consideration of security-related issues bearing on the immediate safety of security personnel or inmates at the county correctional facilities by county correctional superintendents or their designees. 
(h) Consideration of applications by the business finance authority under RSA 162-A:7-10 and 162-A:13, where consideration of an application in public session would cause harm to the applicant or would inhibit full discussion of the application. 
(i) Consideration of matters relating to the preparation for and the carrying out of emergency functions, including training to carry out such functions, developed by local or state safety officials that are directly intended to thwart a deliberate act that is intended to result in widespread or severe damage to property or widespread injury or loss of life. 
(j) Consideration of confidential, commercial, or financial information that is exempt from public disclosure under RSA 91-A:5, IV in an adjudicative proceeding pursuant to RSA 541 or RSA 541-A. 
III. Minutes of meetings in nonpublic session shall be kept and the record of all actions shall be promptly made available for public inspection, except as provided in this section. Minutes and decisions reached in nonpublic session shall be publicly disclosed within 72 hours of the meeting, unless, by recorded vote of 2/3 of the members present, it is determined that divulgence of the information likely would affect adversely the reputation of any person other than a member of the public body itself, or render the proposed action ineffective, or pertain to terrorism, more specifically, to matters relating to the preparation for and the carrying out of all emergency functions, developed by local or state safety officials that are directly intended to thwart a deliberate act that is intended to result in widespread or severe damage to property or widespread injury or loss of life. This shall include training to carry out such functions. In the event of such circumstances, information may be withheld until, in the opinion of a majority of members, the aforesaid circumstances no longer apply.

There was no VOTE to go into nonpublic session. There was no reason given under RSA 91-A, only that “there are two lawyers present so it’s legal.”