You can turn on search match highlights like this.
To turn it off until the next time you search, use this.
To change highlight to a specific color:
:hi Cursor guibg=#rrggbb
:hi Search guibg=<colorname>
You can do this with the vim-gitgutter plugin. If you're not using git, then Signify has a similar feature.
After installing vim-gitgutter, you can switch the highlighting on and off with the following commands:
turn on with :GitGutterLineHighlightsEnable
turn off with :GitGutterLineHighlightsDisable
toggle with :GitGutterLineHighlightsToggle.
Or, to ...