A retainer is a set monthly fee for you to take charge of a service or for responding to and fixing/repairing/updating/sorting your customers' issues/problems/changes out.
An hourly rate is where you add up your time spent per week (say) and invoice them per hour.
The benefit for the customer of a retainer is that they know what your role is (as specified in your specifications of what is covered and what is not) and what the running cost to the business is. They don't then have to consider how much it will cost to do A or B or bother with time-consuming quotes and job estimates.
The benefit to you of a retainer is that you know what this customer is worth each and every month to you, and although some months will be heavy (i.e., your hourly rate in effect drops), other months will be light (i.e., in effect, your hourly rate goes up).
I would strongly suggest you get as many customers on retainer as possible. This is far better than an hourly rate for your business and for your customer IMHO.
A good retainer model I use is where I update my customers' sites for them. I provide an issue tracker for them so they can raise a support ticket for say, "Can you add this PDF to the downloads page" and I can respond with questions for clarity or with a completed message. This acts not only as a clear work log, but a measure of response times from me to them for instance.
For items not covered in our agreement (such as advising on their PPC campaigns), I sometimes choose to do it for them anyway (if it is a light month) or respond with a quote for the work to be completed. Some customers just email in any requests as it is quicker and easier for them but I add them myself to the ticket system just for a complete record.
My retainer agreement specifies their monthly fee, what the support desk is for and what it covers, and a maximum amount of requests or time spent by me for them. In the background, I keep a private tally for the year (the term of their agreement) and get worried only if it is too light to justify their next year commitment or too big so that I am spending too much time on it.
With two or three retainers you can start looking to take on an employee to cover the workload, while you get on with finding more customers.
Retainers are great. Personally, I love them, and try my best to get every customer on them. Just make sure the price is attractive to the customer, because retainers can see you through those times when the more interesting or profitable project work dries up.