Something soothing is comforting; it helps calm fears, anxiety, or pain. Cool aloe vera lotion is very soothing on a really bad sunburn, while pacifiers are soothing to screaming babies.
The adjective soothing comes to us from the verb soothe, which means "to relieve." So something soothing brings relief and makes you feel better. Soothing music can help you feel more relaxed, while a soothing cup of hot chocolate can warm you up from the frigid cold. And if you fall and scrape your knee? You'll probably wish your mom was there to offer some soothing words and a kiss to make it all better.