When you want to write some simple log in the client, you can use console.log('...') API as you know. But it's not supported by all browsers and your script may be broken. So, you should check it first if console is available. Also, you may want to write logs somewhere else. Even you may want to write logs in some level. ASP.NET Boilerplate defines safe logging functions:

abp.log.debug('...');
abp.log.info('...');
abp.log.warn('...');
abp.log.error('...');
abp.log.fatal('...');

You can change log level by setting abp.log.level to one of abp.log.levels (ex: abp.log.levels.INFO to do not write debug logs). These functions write logs to browser's console by default. But you can override/extend this behaviour if you need.