图片的父容器position设置为relative。文字position设置为absolute。
.thumbnail {
position: relative;
}
.caption {
position: absolute;
top: 45%;
left: 0;
width: 100%;
}
示例：
<!DOCTYPE html>
<html lang="zh">
<head>
<title>Bootstrap图片内显示文字</title>
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/4.0.0/css/bootstrap.min.css" integrity="sha384-Gn5384xqQ1aoWXA+058RXPxPg6fy4IWvTNh0E263XmFcJlSAwiGgFAW/dAiS6JXm" crossorigin="anonymous">
<style type="text/css">
.thumbnail {
position: relative;
}
.caption {
position: absolute;
top: 45%;
left: 0;
width: 100%;
}
</style>
</head>
<body>
<div class="row" id="box-search">
<div class="thumbnail text-center">
<img src="img/hello_world.png" alt="" class="img-responsive">
<div class="caption">
<p>世界很大，我想去看看</p>
</div>
</div>
</div>
</body>
</html>