Definition of Connotation:The set of ideas or emotional associations a word suggests.
Example of connotation #1:
And on a day we meet to walk the line
And set the wall between us once again.
We keep the wall between us as we go.
This poem exemplifies connotation in the way "the wall" suggests a distance between the narrator and the other person. Connotation implies meaning beyond the literal definition of a word.
Example of connotation #2:
I hear America singing, the varied carols I hear;
Those of mechanics - each one singing his, as it should be, blithe and strong;
The carpenter singing his, as he measures his plank or beam,
The mason singing his, as he makes ready for work, or leaves off work;
Connotation in this poem exists in the implied meaning of the word "singing". The subjects of the poem may be actually singing, but connotation suggests that Americans are a joyful, spirited people.