Setting your profile to invisible means it won't show up in searches or as being 'online now'. Additionally, your invisible profile can only be viewed by members you have provided access to.
You can change your visibility feature by pressing on the round icon with your profile photo, located on the top right hand corner of the page, select “Account Settings” from the drop-down menu that appears.
Once on the Settings page, go to "Privacy" on the left menu. Untick "I want my profile visible for others to find" and then press "Save Changes".
When accessing via mobile, you may need to press the button which looks like this ≡ to view the left menu.
You can also provide access to members to view your profile, on the Privacy page by adding their username to the text box and press "Add to Visibility List".