A mandatory event does not require any investment decision from you, it is simply for your information. An example of a mandatory event would be a spin-off, where part of a company is spun-off to create a new company. If you have shares in the original company, you will receive shares of the new company whilst retaining your original investment.
A voluntary event invites you to take part in an offer, but you may also decline to take part, in which case the default option will apply. Usually, the default option for a voluntary event is to ‘take no action’. A tender offer is an example of a voluntary event, where a third party wants to buy a portion of equity in your invested company, you will have the option to tender all or part of your investment. The event could eventually become a mandatory takeover where the third party attempts to buy the entire share capital leaving you without the choice to tender or not.