When you want to write a simple log in the client, you can use console.log('...') API as you may already know. However, it's not supported by all browsers and your script may break as a result. You must first check if console is available. You may also want to write logs somewhere else. You may even want to write logs at some other level. ASP.NET Boilerplate defines these safe logging functions:

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

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