Welcome to Android Central! Which device do you have, and which browser are you using? Each time you tap a link to view in the browser, it's probably creating a new tab or browser window (like on your desktop browser). The browser on Android can only have a certain number of browser tabs/windows open at a time, since that all takes up memory. It's a good idea keep the number of open browser tabs under 10 or so.
Usually, there's a tab manager button at the top or bottom of the browser screen--it should look like a square with a number in it, or like a couple of squares overlapping each other. Tap it, and it will show you all of your currently open tabs. Start closing tabs by either swiping them away, or tapping the X at each tab's corner.
If you're using the Chrome browser and you don't see a tab manager, tap the Menu button at the upper right, then Settings, then Merge Tabs and Apps, and make sure that setting is Off. Now look again.