December 2018:
Engaged members are critical to a vibrant Club.  They take initiatives, participate in (or even organize) projects, and magnetize the Club to prospective members.  Conversely, disengaged members take no initiatives, avoid projects (or show up grudgingly), and are a disinterested presence (at best).  Such disengaged members repel prospects spread their disenchantment and eventually threaten the very existence of Clubs, big and small.
The perennial challenge for Club leadership is to make (or keep) members engaged.  Disengaged member will eventually quit the Club, and their unpleasant experience will linger - and be broadcast - for a long time.  Thus, failing to engage members is a disservice to the committed members who seek to “do good in the world”, to advance Rotary ideals, and to benefit the community.
While member engagement has many facets, let’s focus on some key administrative practices that advance or hinder member engagement.  Does the functioning of your Club in all its aspects encourage or discourage member engagement?  Clearly, if you have to pester - or worse, have to resort to “mandates” to compel - members to show up at Club projects/events, you have an acute engagement problem.  And even if your problem is not acute - yet - good Club administrative practices are necessary for member engagement.
Failing to circulate the agenda for Board meetings or the minutes of such meetings is a common failure in many Clubs.  Result?  Members are unaware of Club affairs.  This failure alienates members, who feel no sense of ownership of or responsibility for the Club.  Nothing could be more damaging to members’ sense of involvement, of participation, of engagement in the Club.  Worse, circulating the agenda sufficiently ahead of time also forestalls disasters waiting to happen.  
For example, one such Club’s board approved a member’s proposal to fund what appeared to be a worthwhile project organized by a third party.  Members did not even know about this, except for a terse verbal announcement at the Club meeting with no details.  The project ran aground; the Club’s funds and efforts were wasted.  Imagine the consternation when a member informed them, much after the fiasco, that the third party had been expelled from another Rotary Club.  Would the Club, and the Board, have been well-served by circulating the agenda in advance so that this member could have alerted everyone?  Would the Board have approved the proposal if it had known of the third party’s background or expulsion?  This disaster could have been avoided with a simple step: Circulate the agenda for the Board meeting to the entire membership a week in advance, and do not consider in the meeting any items not so circulated (PDG Arnie Quaranta also recommended this practice in the last District Training Assembly).  In case of genuine emergency - say, disaster relief - the time may be shortened, but the practice should still be adhered to.  It helps member engagement, while also avoiding disasters.
Follow that up by circulating the minutes of the Board meeting promptly.  Ideally, draft minutes should be circulated to the Board within 24 hours of the meeting, and deemed approved absent corrections within 24 hours - so that the minutes may be circulated to the entire membership within 48 hours of the Board meeting.  Let members know of Club developments as they occur or are about to occur, not what’s history.  The minutes don’t have to be exhaustive, just a list of decisions taken.
So also, any material expenditure of the Club funds - say, above $500 - must require board approval at a formal meeting.  In addition to letting members know the items the Board will consider, it will also enable and encourage members who may have special knowledge on specific items to bring it to the Board’s attention.  Maybe there’s a better way to accomplish one or more steps involved, maybe one or more items could be obtained through donation or at discounted prices.  It’s members’ money, why keep them in the dark?
These practices are especially significant for Clubs having a tax-exempt 501(c)(3) Foundation, for which they raise funds from the public. Contemporaneous documentation of projects approved, funds allocated and/or disbursed, and full and timely disclosure of such activities can stave off complications and disputes down the road; as anyone who’s had this unfortunate experience can vouch, that can turn out to be extremely messy, time-consuming, and unproductive - or much worse.  And I’m not even talking about investigations by the New York Attorney General’s Charities Bureau or the IRS or NYS Tax Department - a real nightmare.
The primary key to engagement is empowering members: complete transparency, full disclosure, and full democracy in all Club matters.  You should employ these practices (if you don’t already do so), and have them incorporated into your Club bylaws.