You know how we sometimes think of all cats as mean, all dogs as friendly, all lions as proud, all squirrels as excited, all mules as stubborn, and so on? Well, some people think of all sheep as shy, timid, and awkward.
That's why we use the word "sheepish" to describe people who are a little shy, and a little embarrassed. When you're feeling sheepish, or when you're smiling sheepishly, you feel a little weird and a little uncomfortable because people are looking at you and talking to you—but you don't know what to do, and you don't know what to say. Your face might be pink or red, and you might even hide or cover your face.
You might look sheepish if you're dancing all crazy by yourself, and then your friends walk in and see you. You might grin sheepishly if your crush waves at you and blows you a kiss in front of your whole class. And you might exchange a sheepish glance with your best friend after your teacher congratulates you both for earning the highest test scores.