What is Local Search
Local search is simply the ability of search engines to determine that a given search has significant local content and that they know the location of the searcher. This facility has replaced directories such as Yellow Pages.
Thus someone in say Welshpool, looking for a plumber, simply only has to search "plumber" and a list of local plumbers is included in the search, in Google's case the "3 Pack".
Google Local Search
Entries in the 3 Pack are automatically done by Google in much the same way as the old Yellow Pages, Google will most likely have already entered your business as a Google MyBusiness listing, even if you don't have a website.
For most small businesses, local search will be your best source of free or organic traffic. Working on your GMB listing can generate leads to phone you, ask directions to your address or go directly to your own website.
My plumber in Welshpool above, will almost certainly not show in Shrewsbury as that will be swamped by Shrewsbury plumbers, but he should want to be prominent for places in between.
A clock maker on the other hand will show over a much wider local search, as there are far fewer of them.
You can enhance your local search prescence (and hence traffic) by adding posts and pictures to your GMB account. You can also pay Google to direct more local traffic to this account.
Google My Business and local search are free services from Google. However if you want help to optimise your account and get more traffic through, this is a service I can offer. My service would also include optimising your Facebook profile, which operates in much the same way within Facebook.
I can provide this service as part of my annual maintenance service for £10 pm. As my Consultation fee is deductable from other services, it is strongly recommended you start with a Consultation as every business being different will have different needs in how to optimise it's internet profile.