Edit in JSFiddle

<section class="header">
  <h1 class="header-title">ナビゲーションサンプルその１</h1>
  <p class="header-sub-title">途中からナビゲーションを固定</p>
  <ul class="header-nav">
    <li><a class="nav-tab" href="#content1">CONTENT1</a></li>
    <li><a class="nav-tab" href="#content2">CONTENT2</a></li>
    <li><a class="nav-tab" href="#content3">CONTENT3</a></li>
    <li><a class="nav-tab" href="#content4">CONTENT4</a></li>
    <li><a class="nav-tab" href="#content5">CONTENT5</a></li>
  </ul>
</section>

<section class="contents">
  <div class="content" id="content1">
    <h2 class="content-title">CONTENT1</h2>
    <p>something about content1</p>
  </div>
  <div class="content" id="content2">
    <h2 class="content-title">CONTENT2</h2>
    <p>something about content2</p>
  </div>
  <div class="content" id="content3">
    <h2 class="content-title">CONTENT3</h2>
    <p>something about content3</p>
  </div>
  <div class="content" id="content4">
    <h2 class="content-title">CONTENT4</h2>
    <p>something about content4</p>
  </div>
  <div class="content" id="content5">
    <h2 class="content-title">CONTENT5</h2>
    <p>something about content5</p>
  </div>
</section>

.header,
.content {
	display: flex;
	flex-direction: column;
	justify-content: center;
	align-items: center;
	text-align: center;
	position: relative;
	height: 100vh;
	background: #eee;
	
	.header-title,
	.content-title {
		font-size: 1.5rem;
		margin: 0;
		letter-spacing: 0.5rem;
	}
	.header-sub-title {
		font-size: 1.0rem;
		opacity: 0.6;
	}
}

.header-nav {
	display: flex;
	position: absolute;
	bottom: 0;
	width: 100%;
	height: 70px;
	box-shadow: 0 0 20px rgba(0, 0, 0, 0.1);
	background: #fff;
	z-index: 10;
	li {
		flex: 1;
		height: 100%;
	}
	&.fixed {
		position: fixed;
		top: 0;
	}
}

.nav-tab {
	display: flex;
	justify-content: center;
	align-items: center;
	color: #000;
	letter-spacing: 0.1rem;
	transition: all ease-in-out 0.5s;
	font-size: 0.8rem;
	height: 100%;
	text-decoration: none;
	&:hover {
		color: #fff;
		background: #79c3bf;
		transition: all ease-in-out 0.5s;
	}
}

let _window = $(window),
    _nav = $('.header-nav'),
    headerBottom = $('.header').height() - $('.header-nav').height();

_window.on('scroll', function() {
  if (_window.scrollTop() > headerBottom) {
    _nav.addClass('fixed');
  } else {
    _nav.removeClass('fixed');
  }
});

_window.trigger('scroll');