A hash table has some parts that are ordered, such as the list of buckets, but you very rarely access them in that order because that order has little to no correlation with any useful part of your data.
Say you want to store a lot of strings. If your goal is to efficiently pull out the 73rd (or other arbitrarily selected) string, then you might use an array, which is ordered. Then getting the 73rd string is a matter of referencing the 73rd element in the array directly.
However, say your goal is to efficiently determine if a particular string is in your set. If you have an unsorted array, you need to search through them all of the strings. If you have a sorted array then you need to sort through log(n) of the strings, which is better but still not great. So the solution is a hash table.
Naively... You make an array with 256 entries (each representing one character), each pointing to a list or array of strings that start with that character. Now if you want to find out if "Bob" is in your set of strings, you immediately jump to the 'B' bucket and only look through those strings.
Of course, this example still means you get the strings out in alphabetical order, which sounds nice, but in the real world you would use a hash function more complex than "the first character", preferably one that distributes strings as evenly as possible between your buckets. The result of which is that simply reading through your hash table in order will give you a pseudo-random ordering of your strings.