To update the theme install Envato Market Plugin ( https://github.com/envato/wp-envato-market ). Here is a tutorial how to use this plugin to update your theme: http://www.wpexplorer.com/envato-market-plugin-guide/.
You can also use FTP method and replace files located in the "wp-content/themes/big_gallery_wp" folder.
You won't lost your data (theme options/pages etc) but it's always advised to do backup before updating the theme. You can use some backup plugin like https://wordpress.org/plugins/updraftplus/