Hey, this is quite easy to explain!
儿 has two main meanings. The first, as you correctly stated, is "child" or "son". 儿子 - son, 女儿 - daughter. Note that when it carries this "child" meaning, the 儿 is pronounced as a separate syllable.
Now, the second meaning is a "diminutive suffix", which is linguistic nonsense. It basically means that you can add it onto the ends of words (NOT ALL WORDS!!!) to make the object sound smaller and/or cute - this is common in the north of China, essentially in and around 北京 and 东北. When you add the 儿 in these situations, it usually blends in with the last syllable, and doesn't add an extra syllable.
Examples:
鱼 - fish / 鱼儿 - small cute little fish
羊 - sheep / 羊儿 - small, cute and fluffy little lamb/sheep
冰棍儿 - small ice cream or a popsicle (I don't know if they say 冰棍 in Taiwan or the south of China, but to me it sounds stupid and like you have a giant ice cream).
小孩 - child / 小孩儿 - northern Chinese way to say "child"
花 - flower / 花儿 - flower
鸟 - bird / 鸟儿 - bird
蝴蝶 - butterfly / 蝴蝶儿 - butterfly