The difference is that when you use a Sequence it will only run the functions if you iterate over the elements. So for example this:
val numbers = 1 .. 50
val output = numbers.asSequence().filter{
    println("Filtering $it")
    it < 10
}.map{
    println("Mapping $it")
    Pair("Kotlin", it)
}
will print nothing, because you did not iterate over output.
Checking the docs helps:
/**
 * Creates a [Sequence] instance that wraps the original collection
 * returning its elements when being iterated.
 */
public fun <T> Iterable<T>.asSequence(): Sequence<T> {
    return Sequence { this.iterator() }
}
Using Sequences is useful because if you just call map on a Collection the result will be converted to a List and with a Sequence you can avoid these conversion steps. Think about Sequences like Streams in the Java Stream API (with the difference that Kotlin's solution does not support parallel execution).