People can encounter poetry without realizing it. Poetry appears in many places in life besides places where it is specifically defined as poetry (like on a blog like this one or in a poetry book like First Try).
One obvious example is greeting cards. Anytime you read a greeting card with a beat or a rhyme, you are reading a poem.
Songs are also poetry. There are a number of songs, where if you wrote them out, and read them line by line without the beat or rhythm, they would sound like poems.
Poems also appear in advertising. Think of advertising jingles or any advertisement with a rhyme.
Some jokes are poems. Sometimes a beat, rhyme or pun gives a joke a poetic quality (although not a serious one).
Literary prose can also have poetic qualities at times. If you take certain sections of certain literary prose, and write them with line breaks, the words can sound like poems.
Children’s books are sometimes written as poems. There are a number of children’s stories that rhyme, and there are some that have beat and meter.
Protest chants are sometimes poems. Some of them you hear will have a beat and or a rhyme.
Religious writing often can contain poems. Sometimes the writing is labeled as such, but in other instances it might not be.
If you listen and read closely, you can actually hear and see poetry around you in places where you might not realize it is.