If I name my HTML file "Banks.html" located at www.example.com/Banks.html, but all the content is about Cats and all my other SEO tags are about Cats on the page, will it affect my page's SEO?
Can you name your files whatever you want, as long as you have the page title, description, and the rest of the SEO done properly?
If you want to be on better place when someone searchs for 'banks', then yes, it can help you. But unless you are creating pages about cats in banks I'm sure that this wont help you very much :)
Under circumstances this can be considered a black-hat SEO technique. Watch out not to be caught or reported by curious users.
Ideally, your page name should be relevant to the content of the page - so your ranking may improve if you call the page "cats.html", as that is effectively another occurrence of the keyword in the page.
Generally, this is fairly minor compared to the benefits of decent keywords, titles, etc on the page. For more information take a look at articles around Url Strategy, for example:
Page names are often not very representative of the page content (I've seen pages named 7d57As09). Therefore search engines are not going to be particularly upset if the page names appear misleading. However, it's likely that the page name is one of many factors a search engine considers.
If there's no disadvantage in naming a page about cats, "cats.html", then do so! If it doesn't help your SEO, it will make it easier for your visitors!
Naming your pages something meaningful is a good idea and does improve SEO. It's another hint to the search engines what the page is about, in addition to the title and content. You would be surprised if you opened a file on your computer called "Letter to Grandma.doc" and it was actually your tax return!
In general, the best URLs are those that simply give a page name and hierarchical structure, without extensions or ID numbers. Keep it lowercase and separate words with dashes, like this:
example.com/my-cats
or
example.com/cats/mittens
In your case you will probably wanna keep the .html extension to avoid complexities with URL rewriting.
It shouldn't affect your search engine ranking, but it may influence people who, having completed a search on Google (or some of the other great search engines, like um...uh...), are now scanning the results to decide where to click first. Someone faced with a url like www.dummy.com/banks.html would be more likely to click than someone faced with www.dummy.com/default.php?p_id=1&sessid=876492u942fgspw24z because most people haven't a clue what the last part means. It's also more memorable and gives people greater faith in getting back to the same site if you write your URLs nicely. No one that isn't Dustin Hoffman can remember the second URL without a little intense memory training, while everyone can remember banks.html. Just make sure your URL generation is consistent and your rewriting is solid, so you don't end up with loads of page not found errors which can detriment search engine ranking.