Here are some short examples of various textures:
Imitative Polyphony
Example 1
Gustav Mahler, Symphony No. 1 in D major, 3rd Movement
An example of a Canon/Round (like "Row, Row, Row Your Boat"). Listen to how the melody is repeated in different instruments. Does the melody sound familiar?
Example 2
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Johann Sebastian Bach, Fugue in C Minor
In this example, each voice in the fugue is played by a different synthesizer sound
Non-Imitative Polyphony -- where you have simultaneous melodies
Example 1
Madonna, Cherish
Near the end of the record, a second melody appears and is heard through the end of the record as the chorus repeats
Example 2
John Phillip Sousa, Stars and Stripes Forever
The piccolo comes in with a counter-melody while the strings play the main melody
Changing Texture
Whitney Houston, I Will Always Love You
This record is primarily homophonic but it starts with a voice-only monophonic section and becomes homophonic when the instruments come in
Monophonic Texture
Janis Joplin, Mercedes Benz
An example of a monophonic record by a popular music artist. (You could argue that it's not monophonic because there's a hand-clapping or tapping sound accompanying her singing.)
Homophonic Texture
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See if this mixer application makes it easier for you to hear how a popular song is arranged. Listen to some of the individual parts, then listen to the whole mix.