Channel tags (keywords) and the video tags will both help in the search & related video results. For example, if someone searches for channels on "How to tutorials" in the search section, most likely Howcast & ExpertVillage will pop up first but if your channels keywords are related (how,to,tutorials,howto,how-to) your channel will come up somewhere in the results "near" the top hopefully. Same is true with your videos, when a watched video finishes playing related videos pop up. If your video is tagged properly then there is a chance that your video will be shown in the related video section.
However, you can also hurt yourself with too many tags/keywords. Example, lets say someone is watching a video that is tagged (how-to, how, cook spaghetti, recipe, tutorials) and when the video is finished playing related videos will be displayed. If your video is tagged (how-to, how, cook, spaghetti,recipe,tutorials, dogs, cats, boobs, breast, sexy ladies) then there will be no chance your video will be displayed in the recommended or related video section.