Money is worth what other people are willing to trade for it. Some money, like the US dollar and the euro, have a lot of people who are willing to trade goods or services to get it. Since 2009, when Bitcoin was created, it has rapidly attracted people who are interested in using money that cannot be inflated.
Everyone who uses Bitcoin agrees to follow certain rules (that there will only be 21 million Bitcoin, that you can't just say you have more than you really do, etc...). These rules are written down as software and the history of every Bitcoin transaction that followed the rules is recorded in a shared database (that famous blockchain you've heard of).
Sending or receiving Bitcoin is simply using the same rules as everyone else to add a new entry to the database. Every time someone agrees to accept Bitcoin in exchange for something else (dollars, euros, goods or services), they are "backing" Bitcoin with the trade. As long as people are interested in trading to get money which has rules everyone can see, people will want Bitcoin.