A distribution profile is basically a way to make a trust relationship between a particular distribution certificate (which identifies your organisation as a registered Apple development organisation), a particular app or group of apps (identified by an AppID like com.foo.bar.myawesomegame), a set of valid devices where the app can be installed (in the case of ad-hoc distribution; in the case of App Store distribution this is not required), and a set of enabled services, like In-App Purchases.
In your particular situation, if the client wants to test your app, and you are provided with a valid distribution provisioning profile (a file with .mobileprovisioning extension), you also need to install a valid distribution certificate on your computer. The client can download this certificate from http://developer.apple.com (Member Center) and send it to you so you can import it on your machine with a double click on the .cer file.
To enable external users test an app, there's a simpler process, providing that your organisation is a registered Apple development organisation: First, you generate a distribution certificate from http://developer.apple.com. Then, you create a distribution (ad-hoc) provisioning profile and add the distribution certificate and the UUIDs of the iPhones the client wants to use for testing. The client can get the UUIDs from the iTunes app, for example. Then, you can download both the certificate and the distribution profile to your computer, double click to import them into Xcode, and finally sign the app (.ipa file) so that the client can test it on their own devices. You can do that by choosing Product, Archive in Xcode and selecting your distribution certificate and provisioning profile.