With the "Implicit" flow the client (likely a browser) will get a access token, after the Resource Owner (i.e. the user) gave access.
With the "Authorization Code" flow however, the client (usually a web server) does only get an authorization code after the Resource Owner (i.e. the user) gave access. With that authorization code the client then makes another call to the API passing client_id and client_secret together with the authorization code to obtain the access token. All well described here.
Both flows have the exact same result: an access token. However, the "Implicit" flow is much simpler.
The question: Why bother with "Authorization Code" flow, when "Implicit" flow seams to be fine? Why not also using "Implicit" for webserver?
It's more work both for the provider and the client.
tl;dr: This is all because of security reasons.
OAuth 2.0 wanted to meet these two criteria:
Details below:
The implicit flow is only possible in a browser environment because of security reasons:
In the implicit flow the access token is passed directly as a hash fragment (not as a URL parameter). One important thing about hash fragment is that, once you follow a link containing a hash fragment, only the browser is aware of the hash fragment. Browsers will pass the hash fragment directly to the destination webpage (the redirect URI / the client's webpage). Hash fragment have the following properties:
This makes it possible to pass an Access Token directly to the client without the risk of it being intercepted by an intermediary server. This has the caveat of only being possible client side and needs javascript running client side to use the access token.
The implicit flow also has security issues that requires further logic to workaround/avoid for instance:
In the authorization code flow it is not possible to pass an access token directly in a URL parameter because URL parameters are part of the HTTP Request, therefore any intermediary server/routers by which your request would pass (could be hundreds) could be able to read the access token if you are not using en encrypted connection (HTTPS) allowing what's known as Man-in-the-middle attacks.
Passing the access token directly in a URL param could in theory be possible but the auth sever would have to make sure the redirect URI is using HTTPS with TLS encryption and a 'trusted' SSL certificate (typically from a Certificate Authority that is not free) to be sure that the destination server is legitimate and that the HTTP request is fully encrypted. Having all developers purchase an SSL certificate and properly configure SSL on their domain would be a huge pain and would slow adoption down tremendously. This is why an intermediary one-time-use "authorization code" is provided that only the legitimate receiver will be able to exchange (because you need the client secret) and that the code will be useless to potential hackers intercepting the requests over unencrypted transactions (because they don't know the client secret).
You could also argue that the implicit flow is less secure, there are potential attack vectors like spoofing the domain upon redirect - for example by hijacking the IP address of the client's website. This is one of the reasons why the implicit flow only grants access tokens (which are supposed to have a limited time use) and never refresh tokens (which are unlimited in time). To remedy this issue, I advise you to host your webpages on an HTTPS-enabled server whenever possible.