Are you familiar with 'tags' in blogs?
In a blog, a tag is a word that describes what content the particular blog post/article contains. Clicking on a tag allows a reader of the blog to find other posts on the same blog related to that content.
So suppose I'm running a recipe blog website, and I made an article about my yummy Banana Nut Bread, I might 'tag' my article with 'banana' and 'nut' and maybe something like 'teatime' and other words which describe what my post was about. Someone reading my Banana Nut Bread post may want to see what other banana recipes are on my site, so they'd click on my 'banana' tag, and the site will serve them other posts I tagged with 'banana' that the reader may therefore be interested in.
So a hashtag, is the online social network equivalent. To make a hashtag appear, just add a number sign in front of the word you'd like to declare as being a tag.
You familar with Facebook?
Imagine you just visited an awesome website that had a yummy Banana Nut Bread recipe that you'd like to share with your Facebook friends. You'd make a status update, "Guys! I found this amazing Banana Nut Bread recipe! It's #yummy!"
"Yummy," would turn into a hashtag, and other people on Facebook (not necessarily your friends!) who are searching for something 'yummy' might very well find your post. And not just your post, but the link to the website by extension.
I hope as wordy as all of that was ^, it wasn't confusing. Did it help?