The Myers Briggs website defines the differences between Sensing and Intuition by asking these questions: "Do you pay more attention to information that comes in through your five senses (Sensing), or do you pay more attention to the patterns and possibilities that you see in the information you receive (Intuition)?"
Sensors identify with these statements: "Paying attention to physical reality, what I see, hear, touch, taste, and smell. I’m concerned with what is actual, present, current, and real. I notice facts and I remember details that are important to me."
Those who rely on intuition identify with these statements: "Paying the most attention to impressions or the meaning and patterns of the information I get....I remember events more as an impression of what it was like than as actual facts or details of what happened."
Here is one anecdote that demonstrates the difference between a Sensor and an Intuitive:
When we were young, my mom read Bible stories to us from a children's bible. After the story she had us each recount what we could remember. I usually did quite well, (granted I had the advantage of being two years older than my INTJ brother and five years older than the ENFJ one, however they had their own abilities).
I remembered almost all the events and details in the story, even down to specific words. One time, after listening to a shorter story, I began to retell it word for word. Of course I didn't make it all the way to the end like this, but I got most of it word for word with a little help, then my mom read it again and had me try again since I was so close and I got it pretty much spot on. We were all shocked and amazed, myself included.
My INTJ brother had trouble remembering the details. His detail retention was probably about 50% of mine. My mom started to switch up the exercise and asked us to summarize the stories. He was able to summarize a story into a few succinct sentences. I couldn't summarize for the life of me. I was unable to grasp the central thread of the story, the bare bones plot. My best attempt was arbitrarily leaving out details and side-stories which I hated to do. But he found the point of the stories and could extract the major plot-line from amongst the details.
Here's a picture I created to demonstrate. The Sensor sees lots of little details that comprise the big picture. The Intuitive person sees the big picture of which the little pieces are a part of. These are all pictures I took in Iceland at Úlfarsfell.