as simeon mentioned, these notifications and other error messages will usually clear when you restart Splunk. you can do this through the UI by using the Manager > Server controls page where you can either Restart Splunk or Clear Restart Message, which really just refers to clearing the notice that tells you that you have to restart for any changes you made to take effect.
is there a specific notification that you are seeing?
for example, some messages will clear when you change views. like, when you have added data, you will see a message that tells you that the data was successfully saved to an index. and when you click to another page/view, you should no longer see that message.
then, there are notifications that require you to do something. for example, restart Splunk. Or another example, when your license is about to expire, you should see a notice to contact support to renew your license. this notice will remain until you have updated your license.
These errors will typically be cleared by a Splunk restart. Also, there is a way to manually clear the restart notification via the Splunk Web manager interface (Manager > Server Controls).