Most AV Receivers/amps can be considered to be the hub of an AV setup. If you have several sources using the same connection e.g. component video or HDMI, you can run the video via the amp and run a single cable to the TV. Also on newer models, they can upconvert analogue sources (composite, s-video, component video) to HDMI resulting in a single cable to the TV. Some older amps would only upconvert composite video and s-video to component. Upscaling (changing the resolution from one to another) in amps is filtering down all the time to lower priced models but as the scalers fitted in budget receivers aren't much better than the ones found in your TV or source, it is often considered best to leave these to do the scaling. Obviously if you have a higher end amp with a beefy scaling chip, you can use that to scale the image to a suitable resolution e.g. 1080p.
Also note that HDMI also carries video (new version of SCART) so if you want to extract the audio from HDMI, you have to route the video via the Receiver/amp.
My own amp doesn't have HDMI but I do have an external HDMI switch/splitter so that I can feed 3 HDMI sources into 1 and then split that single output to my projector and TV. If I had an AV Receiver with 4 HDMI inputs and 2 outputs, I could do away with these altogether.
Presumably you don't have multiple sources using the same connection type or you have sufficient inputs on your display? If you do and don't need HDMI audio, your present amp is more than sufficient for your present needs.