Backlinks or "incoming links" are links from one website to a page on another website. Generally speaking, someone with a website only posts a link to another site if that other site may be of interest to their own visitors.
If many other websites link to a particular website, then it is logical to assume that that page is important or has very useful information. Therefore, Google, Bing and other search engines consider such links to be "votes" for a particular page. The more links, the more likely it is that that page will rank high in search results.
So if you have a lot of backlinks to your own website, the search engines "think" your site is valuable, otherwise why would they link to it?
Since the beginning of search engines, this has been an important tool for search engines to measure the "importance" of a website, and thus its position in search results. In the beginning, Google called this the Pagerank of and website. The higher the Pagerank, the more important your website was.
Since then, a lot has changed and Google has also adjusted its algorithm, but backlinks still weigh heavily in the search results of search engines.
So are all backlinks valuable?
Besides looking at the number of backlinks, search engines also look at where those links are placed. If there is a link to your website on the website of a university such as Oxford, for example, it will weigh more heavily than a link on a totally unknown page. Focus mainly on high quality links, one good link is worth more than a thousand bad links. But what are good links?
This principle is known as "Domain Authority." Essentially, the more authority a particular website has, the more authority it can pass on to your website (via a link).
Search engines ignore a link that has a 'nofollow' attribute. Many websites give a link a nofollow attribute if it is, for example, a paid link. If they then add a 'nofollow' attribute, this will not help your SEO.
So make sure you have a link without a nofollow attribute.
Anchor text of your link
Another important point is the anchor text in a link. This is the text that you click on. Preferably use a keyword in this anchor text. So don't use "click here" in a link to your website. But use a keyword you want to be found on. If you have a bicycle store in London for example, then create a link like "Bikestore London".
But be careful not to overdo it. Using too many links or anchor texts with too many or too heavy keywords can have a negative effect. So be careful with texts like "best", "cheapest" etc. And don't place too many links to your website on the same page. Such techniques are called 'Black hat' techniques, and will ensure that your website ranks less well in the search engine results.
Thematically similar pages
When a website links to your site it is important that the referring site has (some) similarity in subject matter as your own website. If an information website about bicycles links to your bicycle store website, it is more important than a link on a site about curtains.
Quality of the referring websites
As I wrote above, it is important what kind of website your link is on. But this is also about the page itself. Are you on a 'our friends' page, for example, via link exchange (which is already not recommended, more on this soon), where there are dozens of links to other websites without any content, the value of this link will not be much or even work against your results.
If you are on a news website, where there is a article about your business with a single link to your website, the value of that link will be higher.
Common sense in SEO
SEO seems difficult, but actually it's nothing more than using your common sense. Why does another site rank higher? Because Google thinks that site is better for the visitor. For example, by the content on that site, but also by the backlinks to that website.
But once you start using 'black hat techniques' it may be that you score well temporarily, but in the long run this will always work against you. And then it will be very difficult to get your website to score well again.