Alex has explained it pretty well. For those who still did not get quite a grasp on it, hopefully this example will help you understand:
Lets say I work for Google, in the Chrome team, and I want to add a feature to the browser which notifies the user if the url he has entered is a malicious URL. So I have a dataset of about 1 million malicious URLs, the size of this file being around 25MB. Since the size is quite big, (big in comparison to the size of the browser itself), I store this data on a remote server.
Case 1 : I use a hash function with a hash table. I decide on an efficient hashing function, and run all the 1 million urls through the hashing function to get hash keys. I then make a hash table (an array), where the hash key would give me the index to place that URL. So now once I have hashed and filled the hashing table, I check its size. I have stored all 1 million URLs in the hash table along with their keys. So the size is at least 25 MB. This hash table, due to its size will be stored on a remote server. When a user comes along and enters a URL in the address bar, I need to check if it malicious. Thus I run the URL through the hash function (the browser itself can do this) and I get a hash key for that URL. I now have to make a request to my remote server with that hash key, to check the if the particular URL in my hash table with that particular key, is the same as what the user has entered. If yes then it is malicious and if no then it is not malicious. Thus every time the user enters a URL, a request to the remote server has to be made to check if it is a malicious URL. This would take a lot of time and thus make my browser slow.
Case 2 : I use a bloom filter. The entire list of 1 million URLs are run through the bloom filter using multiple hash functions and the respective positions are marked as 1, in a huge array of 0s. Let's say we want a false positive rate of 1%, using a bloom filter calculator (http://hur.st/bloomfilter?n=1000000&p=0.01) , we get the size of the bloom filter required as only 1.13 MB. This small size is expected as, even though the size of the array is huge, we are only storing 1s or 0s and not the URLs as in case of the hash table.This array can be treated as a bit array. That is, since we have only two values 1 and 0, we can set individual bits instead of bytes. This would reduce the space taken by 8 times. This 1.13 MB bloom filter, due to its small size, can be stored in the web browser itself !! Thus when a user comes along and enters a URL, we simply apply the required hash functions (in the browser itself), and check all the positions in the bloom filter (which is stored in the browser). A value of 0 in any of the positions tells us that this URL is DEFINITELY NOT in the list of malicious URLs and the user can proceed freely. Thus we did not make a call to the server and hence saved time. A value of 1 tells us that the URL MIGHT be in the list of malicious URLs. In these cases we make a call to the remote server and over there we can use some other hash function with some hash table as in the first case to retrieve and check if the URL is actually present.
Since most of the times, a URL is not likely to be a malicious one, the small bloom filter in the browser figures that out and hence saves time by avoiding calls to the remote server. Only in some cases, if the bloom filter tells us that the URL MIGHT be malicious, only in those cases we make a call to the server. That 'MIGHT' is 99% right.
So by using a small bloom filter in the browser, we have saved a lot of time as we do not need to make server calls for every URL entered.
We can see that hash table with a single hash function is used for a different purpose altogether than a bloom filter. Hopefully this clears your doubts :)
edit:
I have implemented a bloom filter for the task of malicious URL testing in Python. The code can be found here - https://github.com/tarunsharma1/Bloom-Filter
The code is very simple to understand and a detailed description is provided in the readme file.
