Backlinks are incoming links to your webpage or ,better said, links pointing to your webpage. In theory, having more backlinks is better for your website, because backlinks are an important factor in how search engines rank your site in their result pages. Pagerank from Google also counts very much on the number of the incoming links, because the more links are pointing to a web page, the higher pagerank it will have assigned.

It is better to have backlinks from websites which are similar in content with yours, because that will add credibility and your website will not get banned from search engines for buying backlinks. Google hates fake backlinks, so make sure you have only good backlinks from sites you trust and with similar content as with yours, or you risk to have your website blacklisted or in best case your website may drop down a lot in SERPs(search engine result position).

Now if you want to check how many backlinks your website has (according to the Yahoo! search engine), i have created a tool to simplify the process. You just have to input the url of the webpage (or the root domain) you want and choose wether you want or not to see PageRank for every backlinks individually and click the check button. You will be shown the total number of the backlinks pointing to the url you specified and only the first 1000 backlinks (if applicable), even if it shows to be more than 1000, because this is the limit of the search results that the Yahoo! search engine returns.

If you want to try the Backlink Checker tool follow this link.