In a nutshell
Moments are the different steps a user is going through when he is trying to solve his Job To Be Done. You can use Mental Models for identifying all key moments a user is going through and try to formulate the best brand experience possible. You can also use the See-Think-Do-Care model (from Google) for helping you when you define these moments. Do you understand your activity through your customer’s eyes?
In the Marketing Canvas
In the Marketing Canvas, we have identified 6 main categories for building your Marketing Strategy: Customers, Brand, Value Proposition, Journey, Conversation and Metrics. Each of these categories, have 4 dimensions which means that a total of 24 dimensions (6 by 4) are defining your Marketing Strategy.
Moments is a one of the 4 dimensions of the Journey category.
How do you use it?
When working on your Marketing Strategy, Moments in Customer Journey represent all macro-steps (group of steps with same objective) a customer is going through when interacting with your company. These steps could be help me discover your product, help me be interested by your product, help me try your product, help me buy your product, help me first use your product, help me use your product, help me pay (if recurrent usage), help me complaint or even help me leave you (it is always better to quit in good terms).
Moments are also referred as touchpoints in the literature of the Customer Journey (Cx).
It is your operations through customer’s eyes. It is a non linear of divergent and convergent activities. Great customer experiences leave nothing to chance. These moments are what a customer is doing not what you would like them to do.
Google has a framework for Moments called SEE-THINK-DO-CARE but many other formats exist with similar approaches.
Moments are not website, shop nor sales agent. In the past (now more and more companies have understood the importance of Cx), companies were missing some moments. In the car industry (as an example), the moment between ordering the car and receiving the car was not considered in the past. Or it is a very emotional moment because people are waiting for their car and would like to have it as soon as possible. Wrong communication there could arm the brand relationship.
Micro-Moments also exist. It has been described by Google . A micro-moment is an intent-driven decision within a real-time timeframe. A micro-moment can best be explained as an “I need a spare tyre now”, or an “I want a coffee now” moment (more on micro-moments here).
The only way to understand these Moments is to be in the customer’s shoes. Empathy, Observation (or Ethnography) will definitely help you.
How could you identify these moments?
Start from the guest (user/buyer/client/…), from your customer, don’t forget Job-To-Be-Done, Aspirations, Pains & Gains and Engagement.
Build the mental model map 
Group elements in key Moments, moments having similar objectives.
Understand Feeling/Thinking/Doing state of your guest for each Moment (I want because, I am doing because, I feel )
List places (touchpoints where the guest is going during this Moment)
Are the MOMENTS of your user journey helping you achieve your goals?
Mental Models, Wikipedia, https://en.m.wikipedia.org/wiki/Mental_model